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Yu D, Zhan X, Yang LJ, Jia Y. Theoretical description of logical stochastic resonance and its enhancement: Fast Fourier transform filtering method. Phys Rev E 2023; 108:014205. [PMID: 37583163 DOI: 10.1103/physreve.108.014205] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Accepted: 06/19/2023] [Indexed: 08/17/2023]
Abstract
Over the past decade, dynamic schemes have been proposed for the use of bistable systems in the design of logic devices. A bistable system in a noisy background can operate as a reliable logic gate in a moderate noise level, which is called a logical stochastic resonance (LSR). In this paper, we theoretically explore the emergence of LSR in general bistable systems and identify the dynamical mechanisms of LSR. The timescale relationship between the measured time and the mean first-pass time of two-state transitions is a key condition in determining whether the system is reliable. Furthermore, we demonstrate that the stability of the logic operation can be significantly improved by choosing the appropriate filtering method. Low-pass filtered noise-driven systems are more stable than Gaussian white noise. However, band-pass and high-pass filtered noise are harmful to the stability of the system due to the filtering of low-frequency components. Our theoretical and numerical simulation results offer perspectives for the development of logic devices.
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Affiliation(s)
- Dong Yu
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Xuan Zhan
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Li-Jian Yang
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
| | - Ya Jia
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
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2
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Numerical and Experimental Data of the Implementation of Logic Gates in an Erbium-Doped Fiber Laser (EDFL). DATA 2022. [DOI: 10.3390/data8010007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
In this article, the methods for obtaining time series from an erbium-doped fiber laser (EDFL) and its numerical simulation are described. In addition, the nature of the obtained files, the meaning of the changing file names, and the ways of accessing these files are described in detail. The response of the laser emission is controlled by the intensity of a digital signal added to the modulation, which allows for various logical operations. The numerical results are in good agreement with experimental observations. The authors provide all of the time series from an experimental implementation where various logic gates are obtained.
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3
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Suzuki Y, Asakawa N. Stochastic Resonance in Organic Electronic Devices. Polymers (Basel) 2022; 14:polym14040747. [PMID: 35215663 PMCID: PMC8878602 DOI: 10.3390/polym14040747] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Revised: 02/07/2022] [Accepted: 02/09/2022] [Indexed: 01/27/2023] Open
Abstract
Stochastic Resonance (SR) is a phenomenon in which noise improves the performance of a system. With the addition of noise, a weak input signal to a nonlinear system, which may exceed its threshold, is transformed into an output signal. In the other words, noise-driven signal transfer is achieved. SR has been observed in nonlinear response systems, such as biological and artificial systems, and this review will focus mainly on examples of previous studies of mathematical models and experimental realization of SR using poly(hexylthiophene)-based organic field-effect transistors (OFETs). This phenomenon may contribute to signal processing with low energy consumption. However, the generation of SR requires a noise source. Therefore, the focus is on OFETs using materials such as organic materials with unstable electrical properties and critical elements due to unidirectional signal transmission, such as neural synapses. It has been reported that SR can be observed in OFETs by application of external noise. However, SR does not occur under conditions where the input signal exceeds the OFET threshold without external noise. Here, we present an example of a study that analyzes the behavior of SR in OFET systems and explain how SR can be made observable. At the same time, the role of internal noise in OFETs will be explained.
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4
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Aravind M, Parmananda P, Sinha S. Emergent noise-aided logic through synchronization. Phys Rev E 2022; 104:064207. [PMID: 35030959 DOI: 10.1103/physreve.104.064207] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2021] [Accepted: 11/24/2021] [Indexed: 11/07/2022]
Abstract
In this article, we present a dynamical scheme to obtain a reconfigurable noise-aided logic gate that yields all six fundamental two-input logic operations, including the xor operation. The setup consists of two coupled bistable subsystems that are each driven by one subthreshold logic input signal, in the presence of a noise floor. The synchronization state of their outputs robustly maps to two-input logic operations of the driving signals, in an optimal window of noise and coupling strengths. Thus the interplay of noise, nonlinearity, and coupling leads to the emergence of logic operations embedded within the collective state of the coupled system. This idea is manifested using both numerical simulations and proof-of-principle circuit experiments. The regions in parameter space that yield reliable logic operations were characterized through a stringent measure of reliability, using both numerical and experimental data.
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Affiliation(s)
- Manaoj Aravind
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Sudeshna Sinha
- Indian Institute of Science Education and Research Mohali, Knowledge City, SAS Nagar, Sector 81, Manauli, Punjab, PO 140 306, India
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5
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Aravind M, Sinha S, Parmananda P. Competitive interplay of repulsive coupling and cross-correlated noises in bistable systems. CHAOS (WOODBURY, N.Y.) 2021; 31:061106. [PMID: 34241287 DOI: 10.1063/5.0056173] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2021] [Accepted: 05/25/2021] [Indexed: 06/13/2023]
Abstract
The influence of noise on synchronization has potential impact on physical, chemical, biological, and engineered systems. Research on systems subject to common noise has demonstrated that noise can aid synchronization, as common noise imparts correlations on the sub-systems. In our work, we revisit this idea for a system of bistable dynamical systems, under repulsive coupling, driven by noises with varying degrees of cross correlation. This class of coupling has not been fully explored, and we show that it offers new counter-intuitive emergent behavior. Specifically, we demonstrate that the competitive interplay of noise and coupling gives rise to phenomena ranging from the usual synchronized state to the uncommon anti-synchronized state where the coupled bistable systems are pushed to different wells. Interestingly, this progression from anti-synchronization to synchronization goes through a domain where the system randomly hops between the synchronized and anti-synchronized states. The underlying basis for this striking behavior is that correlated noise preferentially enhances coherence, while the interactions provide an opposing drive to push the states apart. Our results also shed light on the robustness of synchronization obtained in the idealized scenario of perfectly correlated noise, as well as the influence of noise correlation on anti-synchronization. Last, the experimental implementation of our model using bistable electronic circuits, where we were able to sweep a large range of noise strengths and noise correlations in the laboratory realization of this noise-driven coupled system, firmly indicates the robustness and generality of our observations.
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Affiliation(s)
- Manaoj Aravind
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
| | - Sudeshna Sinha
- Indian Institute of Science Education and Research Mohali, Knowledge City, SAS Nagar, Sector 81, Manauli, Punjab P.O. 140306, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
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6
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Ashokkumar P, Sathish Aravindh M, Venkatesan A, Lakshmanan M. Realization of all logic gates and memory latch in the SC-CNN cell of the simple nonlinear MLC circuit. CHAOS (WOODBURY, N.Y.) 2021; 31:063119. [PMID: 34241282 DOI: 10.1063/5.0046968] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Accepted: 05/28/2021] [Indexed: 06/13/2023]
Abstract
We investigate the State-Controlled Cellular Neural Network framework of Murali-Lakshmanan-Chua circuit system subjected to two logical signals. By exploiting the attractors generated by this circuit in different regions of phase space, we show that the nonlinear circuit is capable of producing all the logic gates, namely, or, and, nor, nand, Ex-or, and Ex-nor gates, available in digital systems. Further, the circuit system emulates three-input gates and Set-Reset flip-flop logic as well. Moreover, all these logical elements and flip-flop are found to be tolerant to noise. These phenomena are also experimentally demonstrated. Thus, our investigation to realize all logic gates and memory latch in a nonlinear circuit system paves the way to replace or complement the existing technology with a limited number of hardware.
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Affiliation(s)
- P Ashokkumar
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - M Sathish Aravindh
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - A Venkatesan
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - M Lakshmanan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
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7
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Cheng G, Zheng S, Dong J, Xu Z, Gui R. Effect of time delay in a bistable synthetic gene network. CHAOS (WOODBURY, N.Y.) 2021; 31:053105. [PMID: 34240922 DOI: 10.1063/5.0046373] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Accepted: 04/12/2021] [Indexed: 06/13/2023]
Abstract
The essence of logical stochastic resonance is the dynamic manipulation of potential wells. The effect of time delay on the depth of potential wells and the width of a bistable region can be inferred by logic operations in the bistable system with time delay. In a time-delayed synthetic gene network, time delay in the synthesis process can increase the depth of the potential wells, while that in the degradation process, it can reduce the depth of the potential wells, which will result in a decrease in the width of the bistable region (the reason for time delay to induce logic operations without external driving force) and the instability of the system (oscillation). These two opposite effects imply stretching and folding, leading to complex dynamical behaviors of the system, including period, chaos, bubble, chaotic bubble, forward and reverse period doubling bifurcation, intermittency, and coexisting attractors.
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Affiliation(s)
- Guanghui Cheng
- Department of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430048, China
| | - Shutao Zheng
- Department of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430048, China
| | - Jiahao Dong
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - Zhenqin Xu
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - Rong Gui
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
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8
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Phogat R, Ray A, Parmananda P, Ghosh D. Phase coalescence in a population of heterogeneous Kuramoto oscillators. CHAOS (WOODBURY, N.Y.) 2021; 31:041104. [PMID: 34251244 DOI: 10.1063/5.0050451] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 04/01/2021] [Indexed: 06/13/2023]
Abstract
Phase coalescence (PC) is an emerging phenomenon in an ensemble of oscillators that manifests itself as a spontaneous rise in the order parameter. This increment in the order parameter is due to the overlaying of oscillator phases to a pre-existing system state. In the current work, we present a comprehensive analysis of the phenomenon of phase coalescence observed in a population of Kuramoto phase oscillators. The given population is divided into responsive and non-responsive oscillators depending on the position of the phases of the oscillators. The responsive set of oscillators is then reset by a pulse perturbation. This resetting leads to a temporary rise in a macroscopic observable, namely, order parameter. The provoked rise thus induced in the order parameter is followed by unprovoked increments separated by a constant time τPC. These unprovoked increments in the order parameter are caused due to a temporary gathering of the oscillator phases in a configuration similar to the initial system state, i.e., the state of the network immediately following the perturbation. A theoretical framework corroborating this phenomenon as well as the corresponding simulation results are presented. Dependence of τPC and the magnitude of spontaneous order parameter augmentation on various network parameters such as coupling strength, network size, degree of the network, and frequency distribution are then explored. The size of the phase resetting region would also affect the magnitude of the order parameter at τPC since it directly affects the number of oscillators reset by the perturbation. Therefore, the dependence of order parameter on the size of the phase resetting region is also analyzed.
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Affiliation(s)
- Richa Phogat
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
| | - Arnob Ray
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
| | - P Parmananda
- Department of Physics, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India
| | - Dibakar Ghosh
- Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108, India
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9
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Ercan İ, Sütgöl ZD, Özhan FO. Physical Limitations on Fundamental Efficiency of SET-Based Brownian Circuits. ENTROPY 2021; 23:e23040406. [PMID: 33808096 PMCID: PMC8067043 DOI: 10.3390/e23040406] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/31/2021] [Revised: 03/19/2021] [Accepted: 03/24/2021] [Indexed: 11/16/2022]
Abstract
Brownian circuits are based on a novel computing approach that exploits quantum fluctuations to increase the efficiency of information processing in nanoelectronic paradigms. This emerging architecture is based on Brownian cellular automata, where signals propagate randomly, driven by local transition rules, and can be made to be computationally universal. The design aims to efficiently and reliably perform primitive logic operations in the presence of noise and fluctuations; therefore, a Single Electron Transistor (SET) device is proposed to be the most appropriate technology-base to realize these circuits, as it supports the representation of signals that are token-based and subject to fluctuations due to the underlying tunneling mechanism of electric charge. In this paper, we study the physical limitations on the energy efficiency of the Single-Electron Transistor (SET)-based Brownian circuit elements proposed by Peper et al. using SIMON 2.0 simulations. We also present a novel two-bit sort circuit designed using Brownian circuit primitives, and illustrate how circuit parameters and temperature affect the fundamental energy-efficiency limitations of SET-based realizations. The fundamental lower bounds are obtained using a physical-information-theoretic approach under idealized conditions and are compared against SIMON 2.0 simulations. Our results illustrate the advantages of Brownian circuits and the physical limitations imposed on their SET-realizations.
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Affiliation(s)
- İlke Ercan
- Department of Microelectronics, Delft University of Technology, 2628 CD Delft, The Netherlands
- Correspondence:
| | - Zeynep Duygu Sütgöl
- Electrical and Electronics Engineering Department, Boğaziçi University, İstanbul 34342, Turkey; (Z.D.S.); (F.O.Ö.)
| | - Faik Ozan Özhan
- Electrical and Electronics Engineering Department, Boğaziçi University, İstanbul 34342, Turkey; (Z.D.S.); (F.O.Ö.)
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10
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Murali K, Rajasekar S, Aravind MV, Kohar V, Ditto WL, Sinha S. Construction of logic gates exploiting resonance phenomena in nonlinear systems. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200238. [PMID: 33455552 DOI: 10.1098/rsta.2020.0238] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 09/15/2020] [Indexed: 05/22/2023]
Abstract
A two-state system driven by two inputs has been found to consistently produce a response mirroring a logic function of the two inputs, in an optimal window of moderate noise. This phenomenon is called logical stochastic resonance (LSR). We extend the conventional LSR paradigm to implement higher-level logic architecture or typical digital electronic structures via carefully crafted coupling schemes. Further, we examine the intriguing possibility of obtaining reliable logic outputs from a noise-free bistable system, subject only to periodic forcing, and show that this system also yields a phenomenon analogous to LSR, termed Logical Vibrational Resonance (LVR), in an appropriate window of frequency and amplitude of the periodic forcing. Lastly, this approach is extended to realize morphable logic gates through the Logical Coherence Resonance (LCR) in excitable systems under the influence of noise. The results are verified with suitable circuit experiments, demonstrating the robustness of the LSR, LVR and LCR phenomena. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 1)'.
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Affiliation(s)
- K Murali
- Department of Physics, Anna University, Chennai 600 025, India
| | - S Rajasekar
- Department of Physics, Bharathidasan University, Tiruchirapalli 620 024, India
| | - Manaoj V Aravind
- Indian Institute of Science Education and Research Mohali, Sector 81, Manauli PO 140 306, Punjab, India
| | - Vivek Kohar
- The Jackson Laboratory, Bar Harbor, ME 04609, USA
| | - W L Ditto
- Nonlinear Artificial Intelligence Lab, Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
| | - Sudeshna Sinha
- Indian Institute of Science Education and Research Mohali, Sector 81, Manauli PO 140 306, Punjab, India
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11
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Yao Y, Ma J, Gui R, Cheng G. Enhanced logical chaotic resonance. CHAOS (WOODBURY, N.Y.) 2021; 31:023103. [PMID: 33653033 DOI: 10.1063/5.0037032] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 01/11/2021] [Indexed: 06/12/2023]
Abstract
It was demonstrated recently that logical chaotic resonance (LCR) can be observed in a bistable system. In other words, the system can operate robustly as a specific logic gate in an optimal window of chaotic signal intensity. Here, we report that the size of the optimal window of chaotic signal intensity can be remarkably extended by exploiting the constructive interaction of chaotic signal and periodic force, as well as coupling, in a coupled bistable system. In addition, medium-frequency periodic force and an increasing system size can also lead to an improvement in the response speed of logic devices. The results are corroborated by circuit experiments. Taken together, a reliable and rapid-response logic operation can be realized based on periodic force- and array-enhanced LCR.
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Affiliation(s)
- Yuangen Yao
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - Jun Ma
- Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China
| | - Rong Gui
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - Guanghui Cheng
- Department of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430048, China
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12
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Wang X, Wei X, Pu D, Huan R. Single-electron detection utilizing coupled nonlinear microresonators. MICROSYSTEMS & NANOENGINEERING 2020; 6:78. [PMID: 34567688 PMCID: PMC8433136 DOI: 10.1038/s41378-020-00192-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2019] [Revised: 06/01/2020] [Accepted: 06/21/2020] [Indexed: 05/29/2023]
Abstract
Since the discovery of the electron, the accurate detection of electrical charges has been a dream of the scientific community. Owing to some remarkable advantages, micro/nanoelectromechanical system-based resonators have been used to design electrometers with excellent sensitivity and resolution. Here, we demonstrate a novel ultrasensitive charge detection method utilizing nonlinear coupling in two micromechanical resonators. We achieve single-electron charge detection with a high resolution up to 0.197 ± 0.056 e / Hz at room temperature. Our findings provide a simple strategy for measuring electron charges with extreme accuracy.
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Affiliation(s)
- Xuefeng Wang
- Department of Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou, 310027 People’s Republic of China
| | - Xueyong Wei
- State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710049 People’s Republic of China
| | - Dong Pu
- Department of Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou, 310027 People’s Republic of China
| | - Ronghua Huan
- Department of Mechanics, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou, 310027 People’s Republic of China
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13
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Sathish Aravindh M, Venkatesan A, Lakshmanan M. Route to logical strange nonchaotic attractors with single periodic force and noise. CHAOS (WOODBURY, N.Y.) 2020; 30:093137. [PMID: 33003915 DOI: 10.1063/5.0017725] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2020] [Accepted: 09/04/2020] [Indexed: 06/11/2023]
Abstract
Strange nonchaotic attractors (SNAs) have been identified and studied in the literature exclusively in quasiperiodically driven nonlinear dynamical systems. It is an interesting question to ask whether they can be identified with other types of forcings as well, which still remains an open problem. Here, we show that robust SNAs can be created by a small amount of noise in periodically driven nonlinear dynamical systems by a single force. The robustness of these attractors is tested by perturbing the system with logical signals, leading to the emulation of different logical elements in the SNA regions.
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Affiliation(s)
- M Sathish Aravindh
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - A Venkatesan
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - M Lakshmanan
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
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14
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Yao Y, Cheng G, Gui R. Periodic and aperiodic force-induced logical stochastic resonance in a bistable system. CHAOS (WOODBURY, N.Y.) 2020; 30:073125. [PMID: 32752650 DOI: 10.1063/5.0009699] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2020] [Accepted: 06/29/2020] [Indexed: 06/11/2023]
Abstract
It was demonstrated recently that there are optimal windows of noise intensity or frequency and amplitude of the periodic driving force, which let a bistable system operate reliably as logic gates. These phenomena are called logical stochastic resonance (LSR). Given that the driving force is not always perfect regular, there may be phase disturbance in driving force; therefore, the Wiener process is used here to model phase disturbance of driving force, and then the effects of phase disturbance on reliability and agility of logic gates are explored in detail. Comparing with the periodic force, the aperiodic force with appropriate intensity phase disturbance can drive a bistable system to yield phenomena similar to LSR in a wider reliable region and can reduce mean switching time to obtain a faster response of logic devices to the input signal. On the other hand, depending on the amplitude and average angular frequency, moderate-intensity phase disturbance may also reduce success probability and increase mean switching time and thus lead to the instability and the slower response of logic devices.
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Affiliation(s)
- Yuangen Yao
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - Guanghui Cheng
- Department of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430048, China
| | - Rong Gui
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
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15
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Kobayashi TJ. Bayesian gates for reliable logical operations under noisy conditions. Phys Rev E 2020; 101:042205. [PMID: 32422804 DOI: 10.1103/physreve.101.042205] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2019] [Accepted: 03/13/2020] [Indexed: 11/07/2022]
Abstract
The reliability of logical operations is indispensable for the reliable operation of computational systems. Since the downsizing of microfabrication generates nonnegligible noise in these systems, a new approach for designing noise-immune gates is required. In this paper, we demonstrate that noise-immune gates can be designed by combining Bayesian inference theory with the idea of computation over noisy channels. To reveal their practical advantages, the performance of these gates is evaluated in comparison with a stochastic resonance-based gate proposed previously. We also demonstrate that, in a high noise-level situation, this approach for computation can be better than a conventional one that conducts information transmission and computation separately.
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Affiliation(s)
- Tetsuya J Kobayashi
- Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba Meguro-ku, Tokyo 153-8505, Japan
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16
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Gui R, Zhang H, Cheng G, Yao Y. Set-reset latch logic operation in a bistable system under suprathreshold and subthreshold signals. CHAOS (WOODBURY, N.Y.) 2020; 30:023119. [PMID: 32113237 DOI: 10.1063/1.5134888] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2019] [Accepted: 01/20/2020] [Indexed: 06/10/2023]
Abstract
A set-reset latch is a basic building block of computers and can be used to store state information. Here, by testing the influence of the two logical input signals on the reliable set-reset latch logic operation in the bistable system, we found that there are two types of input signals, namely, suprathreshold and subthreshold signals. For the suprathreshold signals, reliable set-reset logic operation can be achieved without any driving forces and exhibits certain anti-interference ability; for the subthreshold signals, a single harmonic could induce correct set-reset latch logic operation but with a narrow optimal parameter region. The introduction of biharmonic-induced set-reset latch logic operation (logical vibrational resonance) could greatly expand the parameter region. Explanations for the above results were provided by taking the logical inputs as the dynamic bias to analyze the dynamic changes in the system. Finally, the results were further verified by circuit simulation and actual hardware circuit.
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Affiliation(s)
- Rong Gui
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - Huiyu Zhang
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
| | - Guanghui Cheng
- Department of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430048, China
| | - Yuangen Yao
- Department of Physics, College of Science, Huazhong Agricultural University, Wuhan 430070, China
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17
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Franzke B, Kosko B. Noise can speed Markov chain Monte Carlo estimation and quantum annealing. Phys Rev E 2019; 100:053309. [PMID: 31869933 DOI: 10.1103/physreve.100.053309] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/16/2016] [Indexed: 11/07/2022]
Abstract
Carefully injected noise can speed the average convergence of Markov chain Monte Carlo (MCMC) estimates and simulated annealing optimization. This includes quantum annealing and the MCMC special case of the Metropolis-Hastings algorithm. MCMC seeks the solution to a computational problem as the equilibrium probability density of a reversible Markov chain. The algorithm must cycle through a long burn-in phase until it reaches equilibrium because the Markov samples are statistically correlated. The special injected noise reduces this burn-in period in MCMC. A related theorem shows that it reduces the cooling time in simulated annealing. Simulations showed that optimal noise gave a 76% speed-up in finding the global minimum in the Schwefel optimization benchmark. The noise-boosted simulations found the global minimum in 99.8% of trials compared with only 95.4% of trials in noiseless simulated annealing. Simulations also showed that the noise boost is robust to accelerated cooling schedules and that noise decreased convergence times by more than 32% under aggressive geometric cooling. Molecular dynamics simulations showed that optimal noise gave a 42% speed-up in finding the minimum potential energy configuration of an eight-argon-atom gas system with a Lennard-Jones 12-6 potential. The annealing speed-up also extends to quantum Monte Carlo implementations of quantum annealing. Noise improved ground-state energy estimates in a 1024-spin simulated quantum annealing simulation by 25.6%. The quantum noise flips spins along a Trotter ring. The noisy MCMC algorithm brings each Markov step closer on average to equilibrium if an inequality holds between two expectations. Gaussian or Cauchy jump probabilities reduce the noise-benefit inequality to a simple quadratic inequality. Simulations show that noise-boosted simulated annealing is more likely than noiseless annealing to sample high probability regions of the search space and to accept solutions that increase the search breadth.
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Affiliation(s)
- Brandon Franzke
- Center for Quantum Information Science and Technology, Signal and Image Processing Institute, Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California 90089, USA
| | - Bart Kosko
- Center for Quantum Information Science and Technology, Signal and Image Processing Institute, Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California 90089, USA
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Abstract
It is known that the reliable logical response can be extracted from a noisy bistable system at an intermediate value of noise strength when two random or periodic, two-level, square waveform serve as the inputs. The asymmetry of the potential has a very important role and dictates the type of logical operation, such as or or and, exhibited by the system. Here we show that one can construct logic gates with symmetric bistable potential if the two states of the double-well are thermalized with two different heat baths. It has been found that if a given state is kept at a sufficiently low temperature compared to the other, the system shows one kind of logic behavior (say, or). Interestingly, the system's response turns into the other kind (say, and) if the temperature of the initial low-temperature well is increased gradually and the quality of the logical response first improves and then weakens after passing through a maximum at a particular value. However, the reliability of the second kind of logical response (and) is not as good as the first kind (or) and depends on the amplitude of the inputs. Still one can construct both kinds of logic gates with maximum reliability by properly choosing the initial low-temperature well.
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Affiliation(s)
- Moupriya Das
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
| | - Holger Kantz
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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19
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Rungta PD, Meena C, Sinha S. Identifying nodal properties that are crucial for the dynamical robustness of multistable networks. Phys Rev E 2018; 98:022314. [PMID: 30253521 DOI: 10.1103/physreve.98.022314] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Indexed: 06/08/2023]
Abstract
We investigate the collective dynamics of bistable elements connected in different network topologies and estimate the network response to localized perturbations on different classes of nodes by introducing a variant of the concept of multinode basin stability. We show that perturbations on nodes with high closeness and betweeness centrality drastically reduces the capacity of the system to return to the original state. This effect is most pronounced for a star network, where perturbation of the single hub node can destroy the collective state, while the system manages to recover even when a majority of the peripheral nodes are strongly perturbed. This demonstrates the extreme effect of the centrality of the perturbed node on the stability of the network. Further, we exploit the difference in centrality distributions in random scale-free networks with m=1 and m=2 to probe which property most influences the collective dynamics in heterogeneous networks. Significantly, we find clear evidence that the betweeness centrality of the perturbed node is more crucial for dynamical robustness than closeness centrality or degree of the node. This allows us to decide which nodes to safeguard in order to maintain the collective state of a network against targeted localized attacks.
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Affiliation(s)
- Pranay Deep Rungta
- Indian Institute of Science Education and Research Mohali, SAS Nagar, Sector 81, Mohali 140 306, Punjab, India
| | - Chandrakala Meena
- Indian Institute of Science Education and Research Mohali, SAS Nagar, Sector 81, Mohali 140 306, Punjab, India
| | - Sudeshna Sinha
- Indian Institute of Science Education and Research Mohali, SAS Nagar, Sector 81, Mohali 140 306, Punjab, India
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20
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Vijayajayanthi M, Kanna T, Murali K, Lakshmanan M. Harnessing energy-sharing collisions of Manakov solitons to implement universal NOR and OR logic gates. Phys Rev E 2018; 97:060201. [PMID: 30011592 DOI: 10.1103/physreve.97.060201] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2017] [Indexed: 11/07/2022]
Abstract
The energy-sharing collision of bright optical solitons in the Manakov system, governing pulse propagation in high birefringent fiber, is employed theoretically to realize optical logic gates. In particular, we successfully construct (theoretically) the universal NOR gate and the OR gate from the energy-sharing collisions of just four bright solitons which can be well described by the exact bright four-soliton solution of the Manakov system. This construction procedure has important merits such as realizing the two input gates with a minimal number of soliton collisions and possibilities of multistate logic. The recent experiments on Manakov solitons suggest the possibility of implementation of this theoretical construction of such gates and ultimately an all-optical computer.
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Affiliation(s)
- M Vijayajayanthi
- Department of Physics, B. S. Abdur Rahman Crescent Institute of Science and Technology, Chennai-600 048, India
| | - T Kanna
- PG and Research Department of Physics, Bishop Heber College, Tiruchirappalli-620 017, India
| | - K Murali
- Department of Physics, Anna University, Chennai-600 025, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli-620 024, India
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21
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Sathish Aravindh M, Venkatesan A, Lakshmanan M. Strange nonchaotic attractors for computation. Phys Rev E 2018; 97:052212. [PMID: 29906833 DOI: 10.1103/physreve.97.052212] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2018] [Indexed: 06/08/2023]
Abstract
We investigate the response of quasiperiodically driven nonlinear systems exhibiting strange nonchaotic attractors (SNAs) to deterministic input signals. We show that if one uses two square waves in an aperiodic manner as input to a quasiperiodically driven double-well Duffing oscillator system, the response of the system can produce logical output controlled by such a forcing. Changing the threshold or biasing of the system changes the output to another logic operation and memory latch. The interplay of nonlinearity and quasiperiodic forcing yields logical behavior, and the emergent outcome of such a system is a logic gate. It is further shown that the logical behaviors persist even for an experimental noise floor. Thus the SNA turns out to be an efficient tool for computation.
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Affiliation(s)
- M Sathish Aravindh
- PG and Research Department of Physics, Nehru Memorial College (Autonomous), Puthanampatti, Tiruchirappalli 621 007, India
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
| | - A Venkatesan
- PG and Research Department of Physics, Nehru Memorial College (Autonomous), Puthanampatti, Tiruchirappalli 621 007, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
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22
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Zhang L, Zheng W, Song A. Adaptive logical stochastic resonance in time-delayed synthetic genetic networks. CHAOS (WOODBURY, N.Y.) 2018; 28:043117. [PMID: 31906654 DOI: 10.1063/1.5019297] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
In the paper, the concept of logical stochastic resonance is applied to implement logic operation and latch operation in time-delayed synthetic genetic networks derived from a bacteriophage λ. Clear logic operation and latch operation can be obtained when the network is tuned by modulated periodic force and time-delay. In contrast with the previous synthetic genetic networks based on logical stochastic resonance, the proposed system has two advantages. On one hand, adding modulated periodic force to the background noise can increase the length of the optimal noise plateau of obtaining desired logic response and make the system adapt to varying noise intensity. On the other hand, tuning time-delay can extend the optimal noise plateau to larger range. The result provides possible help for designing new genetic regulatory networks paradigm based on logical stochastic resonance.
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Affiliation(s)
- Lei Zhang
- School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210046, People's Republic of China
| | - Wenbin Zheng
- College of Software Engineering, Chengdu University of Information Technology, Chengdu 610225, People's Republic of China
| | - Aiguo Song
- School of Instrument Science and Engineering, Southeast University, Sipailou 2, Nanjing 210096, People's Republic of China
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23
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Zhang L, Zheng W, Xie F, Song A. Effect of the correlation between internal noise and external noise on logical stochastic resonance in bistable systems. Phys Rev E 2017; 96:052203. [PMID: 29347692 DOI: 10.1103/physreve.96.052203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/23/2017] [Indexed: 06/07/2023]
Abstract
Some noisy nonlinear systems could be exploited to operate reliable logic operation in an optimal window of noise intensity, which is termed as logical stochastic resonance (LSR). We investigated the LSR phenomenon in bistable systems when internal noise and external noise are correlated. The LSR effect is evaluated by the success probability of the obtained desired output with various combinations of logic inputs. It is shown that the or-nor, and-nand, and Latch operations still can operate reliably with the correlated internal noise and external noise. A positive correlation strength tends to enhance or-nor logic and suppress and-nand logic. The negative correlation strength tends to suppress or-nor logic and enhance and-nand logic. The results provide possible corroboration for implementing reliable LSR when internal noise and external noise are correlated.
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Affiliation(s)
- Lei Zhang
- School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210046, People's Republic of China
| | - Wenbin Zheng
- College of Software Engineering, Chengdu University of Information Technology, Chengdu 610225, People's Republic of China
| | - Fei Xie
- School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing 210046, People's Republic of China
| | - Aiguo Song
- School of Instrument Science and Engineering, Southeast University, Nanjing 210096, People's Republic of China
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24
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Wang N, Zheng B, Zheng H, Yu Z. Feeble object detection of underwater images through LSR with delay loop. OPTICS EXPRESS 2017; 25:22490-22498. [PMID: 29041558 DOI: 10.1364/oe.25.022490] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Accepted: 08/27/2017] [Indexed: 06/07/2023]
Abstract
Feeble object detection is a long-standing problem in vision based underwater exploration work. However, because of the complicated light propagation situation and high background noise, underwater images are highly degraded. Noise is not always detrimental. Logical stochastic resonance (LSR) can be a useful tool for amplifying feeble signals by utilizing the constructive interplay of noise and a nonlinear system. In the present study, an appropriate LSR structure with a delay loop is proposed to process a low-quality underwater image for enhancing the vision detection accuracy of underwater feeble objects. Ocean experiments are conducted to demonstrate the effectiveness of the proposed structure. We also give explicit numerical results to illustrate the relationship between the structure of LSR and the correct detection probability. Methods presented in this paper are quite general and can thus be potentially extended to other applications for obtaining better performance.
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25
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Venkatesh PR, Venkatesan A, Lakshmanan M. Implementation of dynamic dual input multiple output logic gate via resonance in globally coupled Duffing oscillators. CHAOS (WOODBURY, N.Y.) 2017; 27:083106. [PMID: 28863500 DOI: 10.1063/1.4997758] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We have used a system of globally coupled double-well Duffing oscillators under an enhanced resonance condition to design and implement Dual Input Multiple Output (DIMO) logic gates. In order to enhance the resonance, the first oscillator in the globally coupled system alone is excited by two forces out of which one acts as a driving force and the other will be either sub-harmonic or super-harmonic in nature. We report that for an appropriate coupling strength, the second force coherently drives and enhances not only the amplitude of the weak first force to all the coupled systems but also drives and propagates the digital signals if any given to the first system. We then numerically confirm the propagation of any digital signal or square wave without any attenuation under an enhanced resonance condition for an amplitude greater than a threshold value. Further, we extend this idea for computing various logical operations and succeed in designing theoretically DIMO logic gates such as AND/NAND, OR/NOR gates with globally coupled systems.
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Affiliation(s)
- P R Venkatesh
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Puthanampatti, Tiruchirapalli 621 007, India
| | - A Venkatesan
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Puthanampatti, Tiruchirapalli 621 007, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024, India
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26
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Ando H, Takehara K, Kobayashi MU. Time-delayed feedback control of diffusion in random walkers. Phys Rev E 2017; 96:012148. [PMID: 29347143 DOI: 10.1103/physreve.96.012148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2017] [Indexed: 06/07/2023]
Abstract
Time delay in general leads to instability in some systems, while specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a stochastic process, i.e., a random walk, and observe its diffusion phenomenon with time-delayed feedback. As a result, the diffusion coefficient decreases with increasing delay time. We analytically illustrate this suppression of diffusion by using stochastic delay differential equations and justify the feasibility of this suppression by applying time-delayed feedback to a molecular dynamics model.
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Affiliation(s)
- Hiroyasu Ando
- Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Ten-noudai, Tsukuba 305-8573 Japan
| | - Kohta Takehara
- Department of Business Administration, Graduate School of Social Science, Tokyo Metropolitan University, 1-4-1 Marunouchi, Chiyoda-ku, Tokyo 100-0005, Japan
| | - Miki U Kobayashi
- Faculty of Economics, Rissho University, 4-2-16 Osaki, Shinagawa-ku, Tokyo 141-8602, Japan
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27
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Wu J, Xu Y, Wang H, Kurths J. Information-based measures for logical stochastic resonance in a synthetic gene network under Lévy flight superdiffusion. CHAOS (WOODBURY, N.Y.) 2017; 27:063105. [PMID: 28679222 DOI: 10.1063/1.4984806] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We investigate the logical information transmission of a synthetic gene network under Lévy flight superdiffusion by an information-based methodology. We first present the stochastic synthetic gene network model driven by a square wave signal under Lévy noise caused by Lévy flight superdiffusion. Then, to quantify the potential of logical information transmission and logical stochastic resonance, we theoretically obtain an information-based methodology of the symbol error rate, the noise entropy, and the mutual information of the logical information transmission. Consequently, based on the complementary "on" and "off" states shown in the logical information transmission for the repressive proteins, we numerically calculate the symbol error rate for logic gates, which demonstrate that the synthetic gene network under Lévy noise can achieve some logic gates as well as logical stochastic resonance. Furthermore, we calculate the noise entropy and the mutual information between the square wave signal and the logical information transmission, which reveal and quantify the potential of logical information transmission and logical stochastic resonance. In addition, we analyze the synchronization degree of the mutual information for the accomplished logical stochastic resonance of two repressive proteins of the synthetic gene network by synchronization variances, which shows that those mutual information changes almost synchronously.
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Affiliation(s)
- Juan Wu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Yong Xu
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Haiyan Wang
- School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14412, Germany
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28
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Yadav K, Kamal NK, Shrimali MD. Intermittent feedback induces attractor selection. Phys Rev E 2017; 95:042215. [PMID: 28505827 DOI: 10.1103/physreve.95.042215] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2016] [Indexed: 11/07/2022]
Abstract
We present a method for attractor selection in multistable dynamical systems. It involves a feedback term that is active only when the dynamics of the system is in a particular fraction of state space of the attractor. We implement this method first on a simplest symmetric chaotic flow and then on a bistable neuronal system. We find that adding this space-dependent feedback term to the dynamical equations of these systems will drive the dynamics to the desired attractor by annihilating the other. We further demonstrate that the attractor selection due to this feedback term can be used in construction of logic gates, which is one of the practical applications of the proposed method.
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Affiliation(s)
- Kiran Yadav
- Department of Physics, Central University of Rajasthan, Ajmer 305 817 India
| | - Neeraj Kumar Kamal
- Department of Physics, Central University of Rajasthan, Ajmer 305 817 India
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29
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Venkatesh PR, Venkatesan A, Lakshmanan M. Design and implementation of dynamic logic gates and R-S flip-flop using quasiperiodically driven Murali-Lakshmanan-Chua circuit. CHAOS (WOODBURY, N.Y.) 2017; 27:033105. [PMID: 28364764 DOI: 10.1063/1.4977977] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report the propagation of a square wave signal in a quasi-periodically driven Murali-Lakshmanan-Chua (QPDMLC) circuit system. It is observed that signal propagation is possible only above a certain threshold strength of the square wave or digital signal and all the values above the threshold amplitude are termed as "region of signal propagation." Then, we extend this region of signal propagation to perform various logical operations like AND/NAND/OR/NOR and hence it is also designated as the "region of logical operation." Based on this region, we propose implementing the dynamic logic gates, namely, AND/NAND/OR/NOR, which can be decided by the asymmetrical input square waves without altering the system parameters. Further, we show that a single QPDMLC system will produce simultaneously two outputs which are complementary to each other. As a result, a single QPDMLC system yields either AND as well as NAND or OR as well as NOR gates simultaneously. Then, we combine the corresponding two QPDMLC systems in a cross-coupled way and report that its dynamics mimics that of fundamental R-S flip-flop circuit. All these phenomena have been explained with analytical solutions of the circuit equations characterizing the system and finally, the results are compared with the corresponding numerical and experimental analysis.
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Affiliation(s)
- P R Venkatesh
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Puthanampatti, Tiruchirapalli 621 007, India
| | - A Venkatesan
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Puthanampatti, Tiruchirapalli 621 007, India
| | - M Lakshmanan
- Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024, India
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30
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Wang N, Song A. Enhanced Logical Stochastic Resonance in Synthetic Genetic Networks. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2016; 27:2736-2739. [PMID: 26571540 DOI: 10.1109/tnnls.2015.2495155] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
In this brief, the concept of logical stochastic resonance is applied to implement the Set-Reset latch in a synthetic gene network derived from a bacteriophage λ . Clear Set-Reset latch operation is obtained when the network is only subjected to periodic forcing. The correct probability of obtaining the desired logic operation first increases to unity and then decreases as the amplitude of the periodic forcing increases. In addition, the output logic operation can be easily morphed by tuning the frequency and the amplitude of the periodic forcing. At the same time, we indicate that adding moderate periodic forcing to the background Gaussian noise may increase the length of the optimal plateau of getting the desired logic operation in genetic regulatory network. We also point out that robust Set-Reset latch operation can be obtained using the interplay of periodic forcing and background noise when the noise strength is lower than what is required.
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31
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Zheng B, Wang N, Zheng H, Yu Z, Wang J. Object extraction from underwater images through logical stochastic resonance. OPTICS LETTERS 2016; 41:4967-4970. [PMID: 27805672 DOI: 10.1364/ol.41.004967] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Logical stochastic resonance (LSR), the phenomenon in which the interplay of noise and nonlinearity can raise the accurate probability of response to feeble input signals, is studied in this Lettter to extract objects from highly degraded underwater images. Images captured under water, especially in the turbid areas, always suffer from interference through heavy noise caused by the suspended particles. Inherent noise and nonlinearity cause difficulty in processing these images through conventional image processing methods. However, LSR can optimally address such issues. A heavily degraded image is first extended to a 1D form in the direction determined by the illumination condition, and then normalized to be placed in the LSR system as an input signal. Additional Gaussian noise is added to the system as the auxiliary power to help separate the object and the background. Results in the natural offshore area demonstrate the effect of LSR on image processing, and the proposed method creates an interesting direction in the processing of heavily degraded images.
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32
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Kohar V, Kia B, Lindner JF, Ditto WL. Superlinearly scalable noise robustness of redundant coupled dynamical systems. Phys Rev E 2016; 93:032213. [PMID: 27078350 DOI: 10.1103/physreve.93.032213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2015] [Indexed: 06/05/2023]
Abstract
We illustrate through theory and numerical simulations that redundant coupled dynamical systems can be extremely robust against local noise in comparison to uncoupled dynamical systems evolving in the same noisy environment. Previous studies have shown that the noise robustness of redundant coupled dynamical systems is linearly scalable and deviations due to noise can be minimized by increasing the number of coupled units. Here, we demonstrate that the noise robustness can actually be scaled superlinearly if some conditions are met and very high noise robustness can be realized with very few coupled units. We discuss these conditions and show that this superlinear scalability depends on the nonlinearity of the individual dynamical units. The phenomenon is demonstrated in discrete as well as continuous dynamical systems. This superlinear scalability not only provides us an opportunity to exploit the nonlinearity of physical systems without being bogged down by noise but may also help us in understanding the functional role of coupled redundancy found in many biological systems. Moreover, engineers can exploit superlinear noise suppression by starting a coupled system near (not necessarily at) the appropriate initial condition.
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Affiliation(s)
- Vivek Kohar
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
| | - Behnam Kia
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
| | - John F Lindner
- Physics Department, The College of Wooster, Wooster, Ohio 44691, USA
| | - William L Ditto
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
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33
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Ditto WL, Sinha S. Exploiting chaos for applications. CHAOS (WOODBURY, N.Y.) 2015; 25:097615. [PMID: 26428568 DOI: 10.1063/1.4922976] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
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Affiliation(s)
- William L Ditto
- Department of Physics and Astronomy, University of Hawaii at Mānoa, Honolulu, Hawaii 96822, USA
| | - Sudeshna Sinha
- Indian Institute of Science Education and Research (IISER), Mohali, Knowledge City, Sector 81, SAS Nagar, PO Manauli 140306, Punjab, India
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35
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Das M. Capturing the Landauer bound through the application of a detailed Jarzynski equality for entropic memory erasure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:062120. [PMID: 25615057 DOI: 10.1103/physreve.90.062120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2014] [Indexed: 06/04/2023]
Abstract
The states of an overdamped Brownian particle confined in a two-dimensional bilobal enclosure are considered to correspond to two binary values: 0 (left lobe) and 1 (right lobe). An ensemble of such particles represents bits of entropic information. An external bias is applied on the particles, equally distributed in two lobes, to drive them to a particular lobe erasing one kind of bit of information. It has been shown that the average work done for the entropic memory erasure process approaches the Landauer bound for a very slow erasure cycle. Furthermore, the detailed Jarzynski equality holds to a very good extent for the erasure protocol, so that the Landauer bound may be calculated irrespective of the time period of the erasure cycle in terms of the effective free-energy change for the process. The detailed Jarzynski equality applied to two subprocesses, namely the transition from entropic memory state 0 to state 1 and the transition from entropic memory state 1 to state 1, connects the work done on the system to the probability to occupy the two states under a time-reversed process. In the entire treatment, the work appears as a boundary effect of the physical confinement of the system not having a conventional potential energy barrier. Finally, an analytical derivation of the detailed and classical Jarzynski equality for Brownian movement in confined space with varying width has been proposed. Our analytical scheme supports the numerical simulations presented in this paper.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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36
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Das M. Entropic memory erasure. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032130. [PMID: 24730813 DOI: 10.1103/physreve.89.032130] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2013] [Indexed: 06/03/2023]
Abstract
We have considered a Brownian particle confined in a two-dimensional bilobal enclosure where the state of the particle represents a bit of information having binary value 0 (left lobe) or 1 (right lobe). A time linear force is applied on the particle, driving it selectively to a particular lobe, and thus erasing one bit of information. We explore the statistics of heat and work associated with memory erasure to realize the Landauer limit in the entropic domain. Our results suggest that the mean value of work done associated with the complete erasure procedure satisfies the Landauer bound even when the memory is purely entropic in nature.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
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Kasai S, Tadokoro Y, Ichiki A. Design and characterization of nonlinear functions for the transmission of a small signal with non-Gaussian noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062127. [PMID: 24483406 DOI: 10.1103/physreve.88.062127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2013] [Indexed: 06/03/2023]
Abstract
We design nonlinear functions for the transmission of a small signal with non-Gaussian noise and perform experiments to characterize their responses. Using statistical design theory [A. Ichiki and Y. Tadokoro, Phys. Rev. E 87, 012124 (2013)], a static nonlinear function is estimated from the probability density function of the given noise in order to maximize the signal-to-noise ratio of the output. Using an electronic system that implements the optimized nonlinear function, we confirm the recovery of a small signal from a signal with non-Gaussian noise. In our experiment, the non-Gaussian noise is a mixture of Gaussian noises. A similar technique is also applied to the optimization of the threshold value of the function. We find that, for non-Gaussian noise, the response of the optimized nonlinear systems is better than that of the linear system.
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Affiliation(s)
- Seiya Kasai
- Graduate School of Information Science and Technology, and Research Center for Integrated Quantum Electronics, Hokkaido University, Sapporo 060-0814, Japan
| | | | - Akihisa Ichiki
- Green Mobility Collaborative Research Center, Nagoya University, Nagoya 464-8603, Japan
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Xu Y, Jin X, Zhang H. Parallel logic gates in synthetic gene networks induced by non-Gaussian noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052721. [PMID: 24329310 DOI: 10.1103/physreve.88.052721] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2013] [Indexed: 06/03/2023]
Abstract
The recent idea of logical stochastic resonance is verified in synthetic gene networks induced by non-Gaussian noise. We realize the switching between two kinds of logic gates under optimal moderate noise intensity by varying two different tunable parameters in a single gene network. Furthermore, in order to obtain more logic operations, thus providing additional information processing capacity, we obtain in a two-dimensional toggle switch model two complementary logic gates and realize the transformation between two logic gates via the methods of changing different parameters. These simulated results contribute to improve the computational power and functionality of the networks.
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Affiliation(s)
- Yong Xu
- Department of Applied Mathematics Northwestern Polytechnical University, Xi'an, 710072, China
| | - Xiaoqin Jin
- Department of Applied Mathematics Northwestern Polytechnical University, Xi'an, 710072, China
| | - Huiqing Zhang
- Department of Applied Mathematics Northwestern Polytechnical University, Xi'an, 710072, China
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Hellen EH, Dana SK, Kurths J, Kehler E, Sinha S. Noise-aided logic in an electronic analog of synthetic genetic networks. PLoS One 2013; 8:e76032. [PMID: 24124531 PMCID: PMC3790844 DOI: 10.1371/journal.pone.0076032] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2013] [Accepted: 08/25/2013] [Indexed: 11/29/2022] Open
Abstract
We report the experimental verification of noise-enhanced logic behaviour in an electronic analog of a synthetic genetic network, composed of two repressors and two constitutive promoters. We observe good agreement between circuit measurements and numerical prediction, with the circuit allowing for robust logic operations in an optimal window of noise. Namely, the input-output characteristics of a logic gate is reproduced faithfully under moderate noise, which is a manifestation of the phenomenon known as Logical Stochastic Resonance. The two dynamical variables in the system yield complementary logic behaviour simultaneously. The system is easily morphed from AND/NAND to OR/NOR logic.
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Affiliation(s)
- Edward H. Hellen
- Department of Physics and Astronomy, University of North Carolina Greensboro, Greensboro, North Carolina, United States of America
- * E-mail:
| | - Syamal K. Dana
- Council of Scientific and Industrial Research-Indian Institute of Chemical Biology, Kolkata, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam, Germany
| | - Elizabeth Kehler
- Department of Physics and Astronomy, University of North Carolina Greensboro, Greensboro, North Carolina, United States of America
| | - Sudeshna Sinha
- Indian Institute of Science Education and Research Mohali, SAS Nagar, Mohali, Punjab, India
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Das M, Ray DS. Control of logic gates by dichotomous noise in energetic and entropic systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032122. [PMID: 24125228 DOI: 10.1103/physreve.88.032122] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/12/2013] [Revised: 08/07/2013] [Indexed: 06/02/2023]
Abstract
We consider the stochastic response of a nonlinear dynamical system towards a combination of input signals. The response can assume binary values if the state of the system is considered to be the output and the system can make transitions between two states separated by an energetic or entropic barrier. We show how the input-output correspondence can be controlled by an external exponentially correlated dichotomous noise optimizing the logical response which exhibits a maximum at an intermediate value of correlation time. This resonance manifests itself as a "logical" resonance correlation effect and sets the condition for performance of the stochastic system as a logic gate. The role of asymmetry of the dichotomous noise is examined and the results on numerical simulations are correlated with a two-state model using a master equation approach.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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Reenbohn WL, Mahato MC. Relative stability of dynamical states and stochastic resonance in a sinusoidal potential. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032143. [PMID: 24125249 DOI: 10.1103/physreve.88.032143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2013] [Indexed: 06/02/2023]
Abstract
Recently, stochastic resonance was shown to occur in underdamped periodic potentials at frequencies (of the drive field) close to the natural frequency at the minima of the potentials. In these systems the particle trajectories are not arbitrary at low temperatures but follow the drive field with two definite mean phase differences depending on the initial conditions. The trajectories are thus found to be in only two stable dynamical states. The occurrence of stochastic resonance in the periodic potentials was explained as a consequence of the transitions between these two dynamical states as the temperature was increased. In the present work, we find the range of amplitudes of the drive field over which the dynamical states could be observed in a sinusoidal potential. The variation of the relative stability of the dynamical states as a function of drive-field amplitude is clarified by analyzing the nature of curves characterizing the stochastic resonance as the amplitude is varied within the range.
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Affiliation(s)
- W L Reenbohn
- Department of Physics, North-Eastern Hill University, Shillong-793022, India
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Patterson GA, Fierens PI, García AA, Grosz DF. Numerical and experimental study of stochastic resistive switching. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012128. [PMID: 23410304 DOI: 10.1103/physreve.87.012128] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2012] [Indexed: 06/01/2023]
Abstract
In this paper we study the role of noise in the context of resistive switching phenomena by means of experiments and numerical simulations. Experiments are conducted on a manganite sample. We show that the addition of external Gaussian noise to a small amplitude driving signal yields a contrast ratio between low- and high-resistance states, comparable to that obtained by the application of a large amplitude noiseless signal. Furthermore, excellent agreement between numerical simulation and measurement allows us to study resistive switching under varying input conditions and, thus, properly characterize the beneficial role of noise. We believe these results might be of relevance in the area of memory devices where the large scale of electronic integration renders the presence of noise unavoidable.
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Affiliation(s)
- G A Patterson
- Instituto Tecnológico de Buenos Aires, Avenida E. Madero 399 (C1106ACD), C.A.B.A., Argentina.
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Zhang H, Xu Y, Xu W, Li X. Logical stochastic resonance in triple-well potential systems driven by colored noise. CHAOS (WOODBURY, N.Y.) 2012; 22:043130. [PMID: 23278065 DOI: 10.1063/1.4768729] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
In this work, the logic stochastic resonance (LSR) phenomenon in a class of stochastic triple-well potential systems is investigated. Approximate Fokker-Planck equation is first obtained by using decoupling approximation. Then, we show that LSR can be successfully induced by additive or multiplicative Gaussian colored noise in some cases. In the absence of internal noise, LSR implementation seems impossible for a = 0 (The parameter a characterizes the depth of the potential well) since the two side wells are so deep that the particle cannot hop over the barrier into the middle well when the input signal is 0. With the increasing of a, the optimal noise band to yield flexible logic gates appears and moves to higher level of noise as the correlation time of noise increases. Compared with the Gaussian white noise, the reliable region in the parameter plane of potential depth parameter a and additive noise strength D first expands and then shrinks with increasing noise color. Furthermore, the effects of multiplicative Gaussian colored noise on LSR are investigated. It was found that the flexible and reliable logic behavior can be yielded for a = 0 due to the fact that the multiplicative Gaussian colored noise strongly affects the shape of the potential function. With the increasing of a, i.e., a = 0.25, multiplicative Gaussian white noise cannot yield desired logic behavior. Fortunately, LSR can also be expected by adjusting the correlation time of Gaussian colored noise. It can also be observed that the reliable region in the parameter plane of potential depth parameter a and multiplicative noise strength Q is small for the case of Gaussian white noise and it becomes larger with the increasing of noise color.
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Affiliation(s)
- Huiqing Zhang
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, People's Republic of China.
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Das M, Mondal D, Ray DS. Logic gates for entropic transport. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:041112. [PMID: 23214534 DOI: 10.1103/physreve.86.041112] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/04/2012] [Indexed: 06/01/2023]
Abstract
We consider a Brownian particle that is confined in a two-dimensional enclosure and driven by a combination of input signals. It has been shown that the logic gates can be formed by considering the state of the particle experiencing an entropic barrier as the output signal. For a consistent logical output, it is necessary to optimize the strength of the noise driving the particle for a given system size. The variation of the logical output behavior exhibits a turnover at an optimal value of system size parameter, implying a size resonance condition in entropic transport. The role of a transverse bias field used to tune the transport between the entropy dominated regime and the energy dominated regime is elucidated.
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Affiliation(s)
- Moupriya Das
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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Perrone S, Vilaseca R, Masoller C. Stochastic logic gate that exploits noise and polarization bistability in an optically injected VCSEL. OPTICS EXPRESS 2012; 20:22692-22699. [PMID: 23037419 DOI: 10.1364/oe.20.022692] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We study numerically the dynamics of a vertical-cavity surface-emitting laser (VCSEL) with optical injection and show that the interplay of polarization bistability and noise yields a reliable logic output to two logic inputs. Specifically, by encoding the logic inputs in the strength of the light injected into the suppressed polarization mode of the VCSEL (the so-called 'orthogonal' injection), and by decoding the output logic response from the polarization state of the emitted light, we demonstrate an all-optical stochastic logic gate that exploits the ubiquitous presence of noise. It gives the correct logic output response for as short as 5 ns bit times when the dimensionless spontaneous emission coefficient, β(sp), is within the range 10(-4)-10(-1). Considering that typical values of β(sp) in semiconductor lasers are in the range 10(-5)-10(-4), the VCSEL-based logic gate can be implemented with nowadays commercially available VCSELs, exploiting either their intrinsic noise, or external and background noise sources.
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Affiliation(s)
- Sandro Perrone
- Departament de Fisica i Enginyeria Nuclear, Universitat Politecnica de Catalunya, Colom 11, 08222 Terrassa, Spain.
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Reenbohn WL, Pohlong SS, Mahato MC. Periodically driven underdamped periodic and washboard potential systems: dynamical states and stochastic resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031144. [PMID: 22587075 DOI: 10.1103/physreve.85.031144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2012] [Indexed: 05/31/2023]
Abstract
We have studied the motion of an underdamped Brownian particle in (i) a bistable periodic potential and (ii) washboard potentials subjected to a sinusoidal external field. The particles are shown to be effectively in two dynamical states of their trajectories with distinct amplitudes and phase relationship with the external drive. These dynamical states are stable with fixed energies at low temperatures, but transitions between them take place as the temperature is increased. The average input energy loss to the environment per period of the drive shows a stochastic resonance (SR) peak as a function of temperature for the underdamped system potentials studied. The occurrence of SR in these systems is explained using the statistics of transitions between the two dynamical states.
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Affiliation(s)
- W L Reenbohn
- Department of Physics, North-Eastern Hill University, Shillong, India
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Wu H, Jiang HJ, Hou ZH. Array-enhanced Logical Stochastic Resonance in Coupled Bistable Systems. CHINESE J CHEM PHYS 2012. [DOI: 10.1088/1674-0068/25/01/70-76] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Dari A, Kia B, Bulsara AR, Ditto WL. Logical stochastic resonance with correlated internal and external noises in a synthetic biological logic block. CHAOS (WOODBURY, N.Y.) 2011; 21:047521. [PMID: 22225395 DOI: 10.1063/1.3660159] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Following the advent of synthetic biology, several gene networks have been engineered to emulate digital devices, with the ability to program cells for different applications. In this work, we adapt the concept of logical stochastic resonance to a synthetic gene network derived from a bacteriophage λ. The intriguing results of this study show that it is possible to build a biological logic block that can emulate or switch from the AND to the OR gate functionalities through externally tuning the system parameters. Moreover, this behavior and the robustness of the logic gate are underpinned by the presence of an optimal amount of random fluctuations. We extend our earlier work in this field, by taking into account the effects of correlated external (additive) and internal (multiplicative or state-dependent) noise. Results obtained through analytical calculations as well as numerical simulations are presented.
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Affiliation(s)
- Anna Dari
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona 85287-9709, USA.
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Gupta A, Sohane A, Kohar V, Murali K, Sinha S. Noise-free logical stochastic resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:055201. [PMID: 22181464 DOI: 10.1103/physreve.84.055201] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/08/2011] [Indexed: 05/31/2023]
Abstract
The phenomena of logical stochastic resonance (LSR) was demonstrated recently [Phys. Rev. Lett. 102, 104101 (2009)]: namely, when a bistable system is driven by two inputs it consistently yields a response mirroring a logic function of the two inputs in an optimal window of moderate noise. Here we examine the intriguing possibility of obtaining dynamical behavior equivalent to LSR in a noise-free bistable system, subjected only to periodic forcing, such as sinusoidal driving or rectangular pulse trains. We find that such a system, despite having no stochastic influence, also yields phenomena analogous to LSR, in an appropriate window of frequency and amplitude of the periodic forcing. The results are corroborated by circuit experiments.
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Affiliation(s)
- Animesh Gupta
- Indian Institute of Technology Bombay, Powai, Mumbai, India
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Kia B, Spano ML, Ditto WL. Chaos computing in terms of periodic orbits. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:036207. [PMID: 22060475 DOI: 10.1103/physreve.84.036207] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2010] [Revised: 01/19/2011] [Indexed: 05/31/2023]
Abstract
The complex dynamics of chaotic systems can perform computations. The parameters and/or the initial conditions of a dynamical system are the data inputs and the resulting system state is the output of the computation. By controlling how inputs are mapped to outputs, a specific function can be performed. Previously no clear connection has been drawn between the structure of the dynamics and the computation. In this paper we demonstrate how chaos computation can be explained, modeled, and even predicted in terms of the dynamics of the underlying chaotic system, specifically the periodic orbit structure of the system. Knowing the dynamical equations of the system, we compute the system's periodic orbits as well as its stability in terms of its eigenvalues, thereby demonstrating how, how well, and what the chaotic system can compute.
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Affiliation(s)
- Behnam Kia
- School of Biological and Health Systems Engineering, Arizona State University, Tempe, Arizona 85287-9709, USA
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