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Ashokkumar P, Kabilan R, Sathish Aravindh M, Venkatesan A, Lakshmanan M. Harnessing vibrational resonance to identify and enhance input signals. CHAOS (WOODBURY, N.Y.) 2024; 34:013129. [PMID: 38252785 DOI: 10.1063/5.0169195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 12/21/2023] [Indexed: 01/24/2024]
Abstract
We report the occurrence of vibrational resonance and the underlying mechanism in a simple piecewise linear electronic circuit, namely, the Murali-Lakshmanan-Chua circuit, driven by an additional biharmonic signal with widely different frequencies. When the amplitude of the high-frequency force is tuned, the resultant vibrational resonance is used to detect the low-frequency signal and also to enhance it into a high-frequency signal. Further, we also show that even when the low-frequency signal is changed from sine wave to square and sawtooth waves, vibrational resonance can be used to detect and enhance them into high-frequency signals. These behaviors, confirmed by experimental results, are illustrated with appropriate analytical and numerical solutions of the corresponding circuit equations describing the system. Finally, we also verify the signal detection in the above circuit even with the addition of noise.
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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
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
| | - R Kabilan
- PG & Research Department of Physics, Nehru Memorial College (Autonomous), Affiliated to Bharathidasan University, Puthanampatti, Tiruchirappalli 621 007, India
| | - M Sathish Aravindh
- Department of Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli 620 024, 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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2
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Li S, Wang Z, Yang J, Sanjuán MAF, Huang S, Lou L. Ultrasensitive vibrational resonance induced by small disturbances. CHAOS (WOODBURY, N.Y.) 2023; 33:123111. [PMID: 38055719 DOI: 10.1063/5.0172108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/13/2023] [Accepted: 11/14/2023] [Indexed: 12/08/2023]
Abstract
We have found two kinds of ultrasensitive vibrational resonance in coupled nonlinear systems. It is particularly worth pointing out that this ultrasensitive vibrational resonance is transient behavior caused by transient chaos. Considering a long-term response, the system will transform from transient chaos to a periodic response. The pattern of vibrational resonance will also transform from ultrasensitive vibrational resonance to conventional vibrational resonance. This article focuses on the transient ultrasensitive vibrational resonance phenomenon. It is induced by a small disturbance of the high-frequency excitation and the initial simulation conditions, respectively. The damping coefficient and the coupling strength are the key factors to induce the ultrasensitive vibrational resonance. By increasing these two parameters, the vibrational resonance pattern can be transformed from ultrasensitive vibrational resonance to conventional vibrational resonance. The reason for different vibrational resonance patterns to occur lies in the state of the system response. The response usually presents transient chaotic behavior when the ultrasensitive vibrational resonance appears and the plot of the response amplitude vs the controlled parameters shows a highly fractalized pattern. When the response is periodic or doubly periodic, it usually corresponds to the conventional vibrational resonance. The ultrasensitive vibrational resonance not only occurs at the excitation frequency, but it also occurs at some more nonlinear frequency components. The ultrasensitive vibrational resonance as transient behavior and the transformation of vibrational resonance patterns are new phenomena in coupled nonlinear systems.
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Affiliation(s)
- Shangyuan Li
- Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, People's Republic of China
| | - Zhongqiu Wang
- School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, Jiangsu, People's Republic of China
| | - Jianhua Yang
- Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, People's Republic of China
| | - Miguel A F Sanjuán
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - Shengping Huang
- Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, People's Republic of China
| | - Litai Lou
- Jiangsu Key Laboratory of Mine Mechanical and Electrical Equipment, School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou 221116, Jiangsu, People's Republic of China
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Zhang T, Jin Y, Xu Y, Yue X. Dynamical response and vibrational resonance of a tri-stable energy harvester interfaced with a standard rectifier circuit. CHAOS (WOODBURY, N.Y.) 2022; 32:093150. [PMID: 36182351 DOI: 10.1063/5.0105337] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2022] [Accepted: 09/07/2022] [Indexed: 06/16/2023]
Abstract
This paper investigates the dynamical response and vibrational resonance (VR) of a piecewise electromechanically coupled tri-stable energy harvester (TEH), which is driven by dual-frequency harmonic excitations. To achieve a stable DC output, the TEH is interfaced with a standard rectifier circuit. Using the harmonic balance method combined with the separation of fast and slow variables, a steady-state response together with the analytical expressions of displacement and harvested power is derived. The multi-solution feature in the amplitude-frequency response is observed and can improve the harvesting performance of the TEH under a low-frequency environment. There is an optimal time constant ratio and electromechanical coupled coefficient to maximize the harvested DC power. Meanwhile, the VR phenomenon of the TEH is explored through the response amplitude of the low-frequency input signal, which implies that an appropriate combination can induce the occurrence of VR and improve the rectified voltage. Similarly, the nonlinear stiffness coefficients can be adjusted by changing the magnet distance to induce the appearance of VR. The theoretical solutions are well supported by numerical simulation and experimental verification. Specifically, the theoretical analysis and experimental evidence illustrate that the harvested power under the VR effect is much higher than that without VR.
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Affiliation(s)
- Tingting Zhang
- Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China
| | - Yanfei Jin
- Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China
| | - Yong Xu
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Xiaole Yue
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
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Calim A, Longtin A, Uzuntarla M. Vibrational resonance in a neuron-astrocyte coupled model. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200267. [PMID: 33840211 DOI: 10.1098/rsta.2020.0267] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/28/2020] [Indexed: 05/22/2023]
Abstract
Recent findings have revealed that not only neurons but also astrocytes, a special type of glial cells, are major players of neuronal information processing. It is now widely accepted that they contribute to the regulation of their microenvironment by cross-talking with neurons via gliotransmitters. In this context, we here study the phenomenon of vibrational resonance in neurons by considering their interaction with astrocytes. Our analysis of a neuron-astrocyte pair reveals that intracellular dynamics of astrocytes can induce a double vibrational resonance effect in the weak signal detection performance of a neuron, exhibiting two distinct wells centred at different high-frequency driving amplitudes. We also identify the underlying mechanism of this behaviour, showing that the interaction of widely separated time scales of neurons, astrocytes and driving signals is the key factor for the emergence and control of double vibrational resonance. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.
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Affiliation(s)
- Ali Calim
- Department of Biomedical Engineering, Zonguldak Bulent Ecevit University, Zonguldak, Turkey
| | - Andre Longtin
- Department of Physics, University of Ottawa, Ottawa, Ontario, Canada
| | - Muhammet Uzuntarla
- Department of Biomedical Engineering, Zonguldak Bulent Ecevit University, Zonguldak, Turkey
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Omoteso KA, Roy-Layinde TO, Laoye JA, Vincent UE, McClintock PVE. Acoustic vibrational resonance in a Rayleigh-Plesset bubble oscillator. ULTRASONICS SONOCHEMISTRY 2021; 70:105346. [PMID: 33011444 PMCID: PMC7786605 DOI: 10.1016/j.ultsonch.2020.105346] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/10/2020] [Revised: 08/06/2020] [Accepted: 09/09/2020] [Indexed: 06/11/2023]
Abstract
The phenomenon of vibrational resonance (VR) has been investigated in a Rayleigh-Plesset oscillator for a gas bubble oscillating in an incompressible liquid while driven by a dual-frequency force consisting of high-frequency, amplitude-modulated, weak, acoustic waves. The complex equation of the Rayleigh-Plesset bubble oscillator model was expressed as the dynamics of a classical particle in a potential well of the Liénard type, thus allowing us to use both numerical and analytic approaches to investigate the occurrence of VR. We provide clear evidence that an acoustically-driven bubble oscillates in a time-dependent single or double-well potential whose properties are determined by the density of the liquid and its surface tension. We show both theoretically and numerically that, besides the VR effect facilitated by the variation of the parameters on which the high-frequency depends, amplitude modulation, the properties of the liquid in which the gas bubble oscillates contribute significantly to the occurrence of VR. In addition, we discuss the observation of multiple resonances and their origin for the double-well case, as well as their connection to the low frequency, weak, acoustic force field.
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Affiliation(s)
- K A Omoteso
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria
| | - T O Roy-Layinde
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria
| | - J A Laoye
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Ogun State, Nigeria
| | - U E Vincent
- Department of Physical Sciences, Redeemer's University, P.M.B. 230, Ede, Nigeria; Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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Olusola OI, Shomotun OP, Vincent UE, McClintock PVE. Quantum vibrational resonance in a dual-frequency-driven Tietz-Hua quantum well. Phys Rev E 2020; 101:052216. [PMID: 32575245 DOI: 10.1103/physreve.101.052216] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 05/12/2020] [Indexed: 06/11/2023]
Abstract
We investigate the response of a quantum particle in the Tietz-Hua quantum potential driven by biharmonic fields: a low-frequency force and a very high frequency force. The response is characterized by the occurrence of a maximum in the first-order transition probability amplitude |s|^{2} under the influence of the applied fields. It is shown that in the absence of the high-frequency component of the applied fields, |s|^{2} shows a distinct sequence of resonances, whereas an increase in the amplitude of the high-frequency field induces minima in |s|^{2}. However, the |s|^{2} maximum occurs in the low-frequency regime where it may be considered otherwise weak in the presence of a single harmonic force.
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Affiliation(s)
- O I Olusola
- Department of Physics, University of Lagos, Lagos, Nigeria
| | - O P Shomotun
- Department of Physics, University of Lagos, Lagos, Nigeria
| | - U E Vincent
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
- Department of Physical Sciences, Redeemer's University, Ede, Nigeria
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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Roy-Layinde TO, Laoye JA, Popoola OO, Vincent UE, McClintock PVE. Vibrational resonance in an inhomogeneous medium with periodic dissipation. Phys Rev E 2017; 96:032209. [PMID: 29346993 DOI: 10.1103/physreve.96.032209] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2017] [Indexed: 06/07/2023]
Abstract
The role of nonlinear dissipation in vibrational resonance (VR) is investigated in an inhomogeneous system characterized by a symmetric and spatially periodic potential and subjected to nonuniform state-dependent damping and a biharmonic driving force. The contributions of the parameters of the high-frequency signal to the system's effective dissipation are examined theoretically in comparison to linearly damped systems, for which the parameter of interest is the effective stiffness in the equation of slow vibration. We show that the VR effect can be enhanced by varying the nonlinear dissipation parameters and that it can be induced by a parameter that is shared by the damping inhomogeneity and the system potential. Furthermore, we have apparently identified the origin of the nonlinear-dissipation-enhanced response: We provide evidence of its connection to a Hopf bifurcation, accompanied by monotonic attractor enlargement in the VR regime.
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Affiliation(s)
- T O Roy-Layinde
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - J A Laoye
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria
| | - O O Popoola
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - U E Vincent
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
- Department of Physical Sciences, Redeemer's University, Ede, Nigeria
| | - P V E McClintock
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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Zhu J, Kong C, Liu X. Subthreshold and suprathreshold vibrational resonance in the FitzHugh-Nagumo neuron model. Phys Rev E 2016; 94:032208. [PMID: 27739746 DOI: 10.1103/physreve.94.032208] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2016] [Indexed: 06/06/2023]
Abstract
We study the subthreshold and suprathreshold vibrational resonance in the FitzHugh-Nagumo neuron model. For the subthreshold situation, two cases where the stationary states are equilibrium point and limit cycle are considered, where different natures of vibrational resonance are observed via theoretical and numerical methods. Especially when the frequency of the high-frequency driving force is near the so-called canard-resonance frequency, the firing rate can be significantly enhanced at the presence of noise. For the suprathreshold situation, we show that the local maxima of the response amplitude are located at the transition boundaries of different phase-locking patterns. The minimal required forcing amplitudes of high-frequency signal of the firing onset are just multiples of the spiking frequency. Furthermore, phase portraits and time series show that the presence of the global maxima of the response results from not only the suprathreshold but also the subthreshold phase-locking modes. In spite of the distinct characteristics for two stationary states on subthreshold oscillation, the suprathreshold vibrational resonance showed no qualitative difference between the two cases.
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Affiliation(s)
- Jinjie Zhu
- State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
| | - Chen Kong
- State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
| | - Xianbin Liu
- State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
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Roy-Layinde TO, Laoye JA, Popoola OO, Vincent UE. Analysis of vibrational resonance in bi-harmonically driven plasma. CHAOS (WOODBURY, N.Y.) 2016; 26:093117. [PMID: 27781458 DOI: 10.1063/1.4962403] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The phenomenon of vibrational resonance (VR) is examined and analyzed in a bi-harmonically driven two-fluid plasma model with nonlinear dissipation. An equation for the slow oscillations of the system is analytically derived in terms of the parameters of the fast signal using the method of direct separation of motion. The presence of a high frequency externally applied electric field is found to significantly modify the system's dynamics, and consequently, induce VR. The origin of the VR in the plasma model has been identified, not only from the effective plasma potential but also from the contributions of the effective nonlinear dissipation. Beside several dynamical changes, including multiple symmetry-breaking bifurcations, attractor escapes, and reversed period-doubling bifurcations, numerical simulations also revealed the occurrence of single and double resonances induced by symmetry breaking bifurcations.
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Affiliation(s)
- T O Roy-Layinde
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria
| | - J A Laoye
- Department of Physics, Olabisi Onabanjo University, Ago-Iwoye, Nigeria
| | - O O Popoola
- Department of Physics, University of Ibadan, Ibadan, Nigeria
| | - U E Vincent
- Department of Physical Sciences, Redeemers' University, Ede, Nigeria
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10
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Chizhevsky VN. Noise-induced suppression of nonlinear distortions in a bistable system with biharmonic excitation in vibrational resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:032902. [PMID: 26465535 DOI: 10.1103/physreve.92.032902] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/04/2015] [Indexed: 06/05/2023]
Abstract
This paper is a report of the experimental evidence of suppression of vibrational higher-order harmonics in a bistable vertical-cavity surface-emitting laser driven by two harmonic signals with very different frequencies in the phenomenon of vibrational resonance when an optimal amount of white, Gaussian noise is applied. A quantitative characterization of the suppression is given on the basis of the coefficient of nonlinear distortions. The behavior of the coefficient of nonlinear distortions is studied in wide ranges of the added noise intensity, the dc current, and the amplitude of the harmonic signals. The experimental results are compared with a numerical simulation of a Langevin model showing good agreement.
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Affiliation(s)
- V N Chizhevsky
- B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 220072 Minsk, Belarus
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11
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12
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Chizhevsky VN. Experimental evidence of vibrational resonance in a multistable system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062914. [PMID: 25019858 DOI: 10.1103/physreve.89.062914] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2014] [Indexed: 06/03/2023]
Abstract
Experimental evidence of vibrational resonance in a multistable vertical-cavity surface-emitting laser (VCSEL) is reported. The VCSEL is characterized by a coexistence of four polarization states and driven by low-frequency (LF) and high-frequency (HF) periodic signals. In these conditions a series of resonances on the low frequency depending on the HF amplitude is observed. The location of resonances in a parameter space (dc current, amplitude of HF signal) is experimentally studied. For a fixed value of the dc current an evolution of the resonance curves with an increase of the LF amplitude is experimentally investigated.
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Affiliation(s)
- V N Chizhevsky
- B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 220072 Minsk, Belarus
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13
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Vibrational resonance in the FitzHugh–Nagumo system with time-varying delay feedback. Comput Biol Med 2014; 45:80-6. [DOI: 10.1016/j.compbiomed.2013.11.022] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2013] [Revised: 10/30/2013] [Accepted: 11/26/2013] [Indexed: 11/17/2022]
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Jeevarathinam C, Rajasekar S, Sanjuán MAF. Effect of multiple time-delay on vibrational resonance. CHAOS (WOODBURY, N.Y.) 2013; 23:013136. [PMID: 23556973 DOI: 10.1063/1.4793542] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We report our investigation on the effect of multiple time-delay on vibrational resonance in a single Duffing oscillator and in a system of n Duffing oscillators coupled unidirectionally and driven by both a low- and a high-frequency periodic force. For the single oscillator, we obtain analytical expressions for the response amplitude Q and the amplitude g of the high-frequency force at which resonance occurs. The regions in parameter space of enhanced Q at resonance, as compared to the case in absence of time-delay, show a bands-like structure. For the two-coupled oscillators, we explain all the features of variation of Q with the control parameter g. For the system of n-coupled oscillators with a single time-delay coupling, the response amplitudes of the oscillators are shown to be independent of the time-delay. In the case of a multi time-delayed coupling, undamped signal propagation takes place for coupling strength (δ) above a certain critical value (denoted as δu). Moreover, the response amplitude approaches a limiting value QL with the oscillator number i. We obtain analytical expressions for both δu and QL.
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Affiliation(s)
- C Jeevarathinam
- School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India.
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Yu H, Wang J, Sun J, Yu H. Effects of hybrid synapses on the vibrational resonance in small-world neuronal networks. CHAOS (WOODBURY, N.Y.) 2012; 22:033105. [PMID: 23020444 DOI: 10.1063/1.4729462] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We investigate the effect of vibrational resonance in small-world neuronal networks with hybrid chemical and electrical synapses. It is shown that, irrespective of the probability of chemical synapses, an optimal amplitude of high-frequency component of the signal can optimize the dynamical response of neuron populations to the low-frequency component, which encodes the information. This effect of vibrational resonance of neuronal systems depends extensively on the network structure and parameters, which determine the ability of neuronal networks to enhance the outreach of localized subthreshold low-frequency signal. In particular, chemical synaptic coupling is more efficient than the electrical coupling for the transmission of local input signal due to its selective coupling. Moreover, there exists an optimal small-world topology characterized by an optimal value of rewiring probability, warranting the largest peak value of the system response. Considering that two-frequency signals are ubiquity in brain dynamics, we expect the presented results could have important implications for signal processing in neuronal systems.
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Affiliation(s)
- Haitao Yu
- School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, People's Republic of China
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16
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Yang JH, Zhu H. Vibrational resonance in Duffing systems with fractional-order damping. CHAOS (WOODBURY, N.Y.) 2012; 22:013112. [PMID: 22462988 DOI: 10.1063/1.3678788] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
The phenomenon of vibrational resonance (VR) is investigated in over- and under-damped Duffing systems with fractional-order damping. It is found that the factional-order damping can induce change in the number of the steady stable states and then lead to single- or double-resonance behavior. Compared with vibrational resonance in the ordinary systems, the following new results are found in the fractional-order systems. (1) In the overdamped system with double-well potential and ordinary damping, there is only one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for these new resonance behaviors is the value of the fractional-order satisfies α > 1. (2) In the overdamped system with single-well potential and ordinary damping, there is no resonance, whereas there is a single-resonance for the case of fractional-order damping. The necessary condition for the new result is α > 1. (3) In the underdamped system with double-well potential and ordinary damping, there are double-resonance and one kind of single-resonance, whereas there are double-resonance and two kinds of single-resonance for the case of fractional-order damping. The necessary condition for the new single-resonance is α < 1. (4) In the underdamped system with single-well potential, there is at most a single-resonance existing for both the cases of ordinary and fractional-order damping. In the underdamped systems, varying the value of the fractional-order is equivalent to change the damping parameter for some cases.
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Affiliation(s)
- J H Yang
- School of Mechanical and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, People's Republic of China.
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Yu H, Wang J, Liu C, Deng B, Wei X. Vibrational resonance in excitable neuronal systems. CHAOS (WOODBURY, N.Y.) 2011; 21:043101. [PMID: 22225338 DOI: 10.1063/1.3644390] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
In this paper, we investigate the effect of a high-frequency driving on the dynamical response of excitable neuronal systems to a subthreshold low-frequency signal by numerical simulation. We demonstrate the occurrence of vibrational resonance in spatially extended neuronal networks. Different network topologies from single small-world networks to modular networks of small-world subnetworks are considered. It is shown that an optimal amplitude of high-frequency driving enhances the response of neuron populations to a low-frequency signal. This effect of vibrational resonance of neuronal systems depends extensively on the network structure and parameters, such as the coupling strength between neurons, network size, and rewiring probability of single small-world networks, as well as the number of links between different subnetworks and the number of subnetworks in the modular networks. All these parameters play a key role in determining the ability of the network to enhance the outreach of the localized subthreshold low-frequency signal. Considering that two-frequency signals are ubiquity in brain dynamics, we expect the presented results could have important implications for the weak signal detection and information propagation across neuronal systems.
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Affiliation(s)
- Haitao Yu
- School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, People's Republic of China
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Rajasekar S, Abirami K, Sanjuan MAF. Novel vibrational resonance in multistable systems. CHAOS (WOODBURY, N.Y.) 2011; 21:033106. [PMID: 21974641 DOI: 10.1063/1.3610213] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We investigate the role of multistable states on the occurrence of vibrational resonance in a periodic potential system driven by both a low-frequency and a high-frequency periodic force in both underdamped and overdamped limits. In both cases, when the amplitude of the high-frequency force is varied, the response amplitude at the low-frequency exhibits a series of resonance peaks and approaches a limiting value. Using a theoretical approach, we analyse the mechanism of multiresonance in terms of the resonant frequency and the stability of the equilibrium points of the equation of motion of the slow variable. In the overdamped system, the response amplitude is always higher than in the absence of the high-frequency force. However, in the underdamped system, this happens only if the low-frequency is less than 1. In the underdamped system, the response amplitude is maximum when the equilibrium point around which slow oscillations take place is maximally stable and minimum at the transcritical bifurcation. And in the overdamped system, it is maximum at the transcritical bifurcation and minimum when the associated equilibrium point is maximally stable. When the periodicity of the potential is truncated, the system displays only a few resonance peaks.
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Affiliation(s)
- S Rajasekar
- School of Physics, Bharathidasan University, Tiruchirapalli, Tamilnadu 620 024, India.
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Jeevarathinam C, Rajasekar S, Sanjuán MAF. Theory and numerics of vibrational resonance in Duffing oscillators with time-delayed feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:066205. [PMID: 21797459 DOI: 10.1103/physreve.83.066205] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2010] [Revised: 04/12/2011] [Indexed: 05/31/2023]
Abstract
The influence of linear time-delayed feedback on vibrational resonance is investigated in underdamped and overdamped Duffing oscillators with double-well and single-well potentials driven by both low frequency and high frequency periodic forces. This task is performed through both theoretical approach and numerical simulation. Theoretically determined values of the amplitude of the high frequency force and the delay time at which resonance occurs are in very good agreement with the numerical simulation. A major consequence of time-delayed feedback is that it gives rise to a periodic or quasiperiodic pattern of vibrational resonance profile with respect to the time-delayed parameter. An appropriate time delay is shown to induce a resonance in an overdamped single-well system which is otherwise not possible. For a range of values of the time-delayed parameters, the response amplitude is found to be larger than in delay-time feedback-free systems.
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Affiliation(s)
- C Jeevarathinam
- School of Physics, Bharathidasan University, Tiruchirappalli 620 024, India
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Qin YM, Wang J, Men C, Deng B, Wei XL. Vibrational resonance in feedforward network. CHAOS (WOODBURY, N.Y.) 2011; 21:023133. [PMID: 21721775 DOI: 10.1063/1.3603818] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
This paper investigates vibrational resonance in multi-layer feedforward network (FFN) based on FitzHugh-Nagumo (FHN) neuron model. High-frequency stimuli can improve the input-output linearity of firing rates, especially for the inputs with low firing rate. For FFN network, it is found that high-frequency disturbances play important roles in enhancing the propagation of weak signal through layers. Synfire-enhanced phenomenon of signal propagation is also observed in multi-layers network, when the signal transmission is affected by high-frequency disturbances. Network connections are found to be important for the propagation of weak signal. Besides that, the characteristics of high-frequency stimuli such as heterogeneity and frequency can also modulate the propagation of neural code through layers.
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Affiliation(s)
- Ying-mei Qin
- School of Electrical Engineering and Automation, Tianjin University, Tianjin, China
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