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Pérez-Cervera A, Gutkin B, Thomas PJ, Lindner B. A universal description of stochastic oscillators. Proc Natl Acad Sci U S A 2023; 120:e2303222120. [PMID: 37432992 PMCID: PMC10629544 DOI: 10.1073/pnas.2303222120] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 05/18/2023] [Indexed: 07/13/2023] Open
Abstract
Many systems in physics, chemistry, and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example, linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. Here, we introduce a nonlinear transformation of stochastic oscillators to a complex-valued function [Formula: see text](x) that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. The function [Formula: see text] (x) is the eigenfunction of the Kolmogorov backward operator with the least negative (but nonvanishing) eigenvalue λ1 = μ1 + iω1. The resulting power spectrum of the complex-valued function is exactly given by a Lorentz spectrum with peak frequency ω1 and half-width μ1; its susceptibility with respect to a weak external forcing is given by a simple one-pole filter, centered around ω1; and the cross-spectrum between two coupled oscillators can be easily expressed by a combination of the spontaneous power spectra of the uncoupled systems and their susceptibilities. Our approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators.
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Affiliation(s)
- Alberto Pérez-Cervera
- Department of Applied Mathematics, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, Madrid28040, Spain
| | - Boris Gutkin
- Group for Neural Theory, LNC2 INSERM U960, Département d’Etudes Cognitives, Ecole Normale Supérieure - Paris Science Letters University, Paris75005, France
| | - Peter J. Thomas
- Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, Cleveland, OH44106
| | - Benjamin Lindner
- Bernstein Center for Computational Neuroscience Berlin, Berlin10115, Germany
- Department of Physics, Humboldt Universität zu Berlin, BerlinD-12489, Germany
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2
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Semenov VV, Zakharova A. Multiplexing-based control of stochastic resonance. CHAOS (WOODBURY, N.Y.) 2022; 32:121106. [PMID: 36587355 DOI: 10.1063/5.0123886] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2022] [Accepted: 11/29/2022] [Indexed: 06/17/2023]
Abstract
We show that multiplexing (Here, the term "multiplexing" means a special network topology where a one-layer network is connected to another one-layer networks through coupling between replica nodes. In the present paper, this term does not refer to the signal processing issues and telecommunications.) allows us to control noise-induced dynamics of multilayer networks in the regime of stochastic resonance. We illustrate this effect on an example of two- and multi-layer networks of bistable overdamped oscillators. In particular, we demonstrate that multiplexing suppresses the effect of stochastic resonance if the periodic forcing is present in only one layer. In contrast, multiplexing allows us to enhance the stochastic resonance if the periodic forcing and noise are present in all the interacting layers. In such a case, the impact of multiplexing has a resonant character: the most pronounced effect of stochastic resonance is achieved for an appropriate intermediate value of coupling strength between the layers. Moreover, multiplexing-induced enhancement of the stochastic resonance can become more pronounced for the increasing number of coupled layers. To visualize the revealed phenomena, we use the evolution of the dependence of the signal-to-noise ratio on the noise intensity for varying strength of coupling between the layers.
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Affiliation(s)
- Vladimir V Semenov
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
| | - Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
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3
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Tang A, Wang J. Drastic effects of an inert Pt wire on the redox behavior of the Belousov-Zhabotinsky reaction. CHAOS (WOODBURY, N.Y.) 2022; 32:073111. [PMID: 35907722 DOI: 10.1063/5.0095531] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2022] [Accepted: 06/20/2022] [Indexed: 06/15/2023]
Abstract
This research investigated responses of the Belousov-Zhabotinsky (BZ) reaction to the presence of a chemically inert Pt wire in solution. Experiments showed that connecting the Pt wire to a neutral ground caused a spontaneous drastic shift in the redox potential and might even induce complex behavior. Characterizations using an unstirred ferriin solution demonstrated the formation of a red colored propagating front at the grounded Pt wire, suggesting the reduction of ferriin to ferroin. Measurements with different combinations of electrodes in both stirred and reaction-diffusion media further confirmed the reduction of BZ metal catalysts at the Pt wire and the accompanying oxidation reaction at the reference electrode. The observed drastic change in redox potential and oscillation waveform can be understood based on the passive reduction reaction at the indicator electrode that is connected to the reference electrode through a potential meter. The obtained influence can be further manipulated by adding a resistor between the Pt wire and the neutral ground, making this convenient perturbation method attractive for the study of redox chemical reaction dynamics.
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Affiliation(s)
- Alexander Tang
- Department of Chemistry and Biochemistry, University of Windsor, Windsor, Ontario N9B 3P4, Canada
| | - Jichang Wang
- Department of Chemistry and Biochemistry, University of Windsor, Windsor, Ontario N9B 3P4, Canada
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4
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Sarkar P, Paul S, Ray DS. Subharmonics and superharmonics of the weak field in a driven two-level quantum system: Vibrational resonance enhancement. Phys Rev E 2021; 104:014202. [PMID: 34412231 DOI: 10.1103/physreve.104.014202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2021] [Accepted: 06/09/2021] [Indexed: 11/07/2022]
Abstract
We consider a quantum two-level system in bichromatic classical time-periodic fields, the frequency of one of which far exceeds that of the other. Based on systematic separation of timescales and averaging over the fast motion a reduced quantum dynamics in the form of a nonlinear forced Mathieu equation is derived to identify the stable oscillatory resonance zones intercepted by unstable zones in the frequency-amplitude plot. We show how this forcing of the dressed two-level system may generate the subharmonics and superharmonics of the weak field in the stable region, which can be amplified by optimization of the strength of the high frequency field. We have carried out detailed numerical simulations of the driven quantum dynamics to corroborate the theoretical analysis.
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Affiliation(s)
- Prasun Sarkar
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Shibashis Paul
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
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5
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Chern MS, Watanabe N, Suga K, Okamoto Y, Umakoshi H. Modulation of the Belousov-Zhabotinsky Reaction with Lipid Bilayers: Effects of Lipid Head Groups and Membrane Properties. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:6811-6818. [PMID: 34044542 DOI: 10.1021/acs.langmuir.1c00915] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The Belousov-Zhabotinsky (BZ) reaction is an oscillating reaction due to periodic oscillations that happen in the concentration of some intermediates. Such systems can be applied together with hydrophobic membranes to create an autonomous behavior in artificial systems. However, because of a complex set of reactions happening in such systems, the interferences caused by hydrophobic membranes are not easily understood. In this study, we tested lipid membranes composed of trimethylammonium-propane (TAP) and phosphate (PA) lipids in an attempt to break down how the polar region of phosphatidylcholine (PC) lipid membranes affect the BZ reaction. According to our findings, the trimethylammonium group and membrane fluidity are crucial to change the frequency of oscillations in the reaction. In addition, the results also indicate a possible complexation of cerium ions with membranes with a phosphate head group.
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Affiliation(s)
- Michael S Chern
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 5608531, Japan
| | - Nozomi Watanabe
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 5608531, Japan
| | - Keishi Suga
- Department of Chemical Engineering, Graduate School of Engineering, Tohoku University, 6-6-07, Aoba, Aramaki-aza, Aoba-ku, Sendai, Miyagi 980-8579, Japan
| | - Yukihiro Okamoto
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 5608531, Japan
| | - Hiroshi Umakoshi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 5608531, Japan
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6
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Peters KJH, Geng Z, Malmir K, Smith JM, Rodriguez SRK. Extremely Broadband Stochastic Resonance of Light and Enhanced Energy Harvesting Enabled by Memory Effects in the Nonlinear Response. PHYSICAL REVIEW LETTERS 2021; 126:213901. [PMID: 34114877 DOI: 10.1103/physrevlett.126.213901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 05/04/2021] [Indexed: 06/12/2023]
Abstract
We report the first observation of non-Markovian stochastic resonance (SR), and we discover that memory effects in the nonlinearity extremely enlarge the SR bandwidth. Our experimental system is an oil-filled microcavity which, driven by a continuous wave laser, has memory in its nonlinear optical response. Modulating the cavity length while adding noise to the driving laser, we observe a peak in the transmitted signal-to-noise ratio as a function of the noise variance. Through simulations, we reproduce our observations and extrapolate that the SR bandwidth could be ∼3000 times larger in our cavity than in a Kerr-nonlinear cavity. Experiments evidencing this memory-enhanced bandwidth across two decades are presented. As an extension of our results, we numerically demonstrate an order-of-magnitude enhancement in energy harvesting thanks to a nonlinearity with memory.
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Affiliation(s)
- K J H Peters
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - Z Geng
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - K Malmir
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - J M Smith
- Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH, United Kingdom
| | - S R K Rodriguez
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
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7
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Chern MS, Okamoto Y, Suga K, Watanabe N, Umakoshi H. Changes Caused by Liposomes to the Belousov-Zhabotinsky Reaction. J Phys Chem B 2020; 124:9862-9869. [PMID: 33086793 DOI: 10.1021/acs.jpcb.0c06413] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The Belousov-Zhabotinsky (BZ) reaction has been applied to give autonomous dynamic behaviors to artificial systems. This reaction is conducted in an aqueous system, but it produces some hydrophobic intermediates, such as bromine. On the basis of previous works about reactions in the lipid bilayer, we investigated how liposome membranes (water-oil interface) affect the BZ reaction. Herein diacylglycerophosphocholine (PC) molecules with a variety of hydrocarbon tails were selected as components of liposomes, and the BZ reaction in the presence of the liposomes was characterized. As a result, membrane fluidity was the main characteristic leading to changes in the reaction behavior. The decrease of the frequency of oscillations was relevant to membrane fluidity, suggesting the interaction of bromine species in the hydrophobic site of the liposomes. In addition, the heterogeneous membrane (so+ld) of DMPC showed a fast decrease in the amplitude of oscillations. Conclusively, characteristics of the hydrophobic environment play a role in the reaction.
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Affiliation(s)
- Michael S Chern
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 5608531, Japan
| | - Yukihiro Okamoto
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 5608531, Japan
| | - Keishi Suga
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 5608531, Japan
| | - Nozomi Watanabe
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 5608531, Japan
| | - Hiroshi Umakoshi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka 5608531, Japan
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8
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Lawson HS, Holló G, Horvath R, Kitahata H, Lagzi I. Chemical Resonance, Beats, and Frequency Locking in Forced Chemical Oscillatory Systems. J Phys Chem Lett 2020; 11:3014-3019. [PMID: 32216274 PMCID: PMC7311084 DOI: 10.1021/acs.jpclett.0c00586] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2020] [Accepted: 03/27/2020] [Indexed: 06/10/2023]
Abstract
Resonance, beats, and synchronization are general and fundamental phenomena in physics. Their existence and their in-depth understanding in physical systems have led to several applications and technological developments shaping our world today. Here we show the existence of chemical resonance, chemical beats, and frequency locking phenomena in periodically forced pH oscillatory systems (sulfite-hydrogen peroxide and sulfite-formaldehyde-gluconolactone pH oscillatory systems). Periodic forcing was realized by a superimposed sinusoidal modulation on the inflow rates of the reagents in the continuous-flow stirred tank reactor. The dependence of the time period of beats follows the relation known from classical physics for forced physical oscillators. Our developed numerical model describes qualitatively the resonance and beat phenomena experimentally revealed. Application of periodic forcing in autonomously oscillating systems can provide new types of oscillators with a controllable frequency and new insight into controlling irregular chemical oscillation regimes.
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Affiliation(s)
- Hugh Shearer Lawson
- Department
of Physics, Budapest University of Technology
and Economics, Budafoki út 8, H-1111 Budapest, Hungary
| | - Gábor Holló
- MTA-BME
Condensed Matter Research Group, Budapest
University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary
| | - Robert Horvath
- Nanobiosensorics
Group, Institute of Technical Physics and Materials Science, Centre for Energy Research, Konkoly Thege M. u. 29-33, H-1121 Budapest, Hungary
| | - Hiroyuki Kitahata
- Graduate
School of Science, Chiba University, Yayoi-cho 1-33,
Inage-ku, Chiba 263-8522, Japan
| | - István Lagzi
- Department
of Physics, Budapest University of Technology
and Economics, Budafoki út 8, H-1111 Budapest, Hungary
- MTA-BME
Condensed Matter Research Group, Budapest
University of Technology and Economics, Budafoki út 8, H-1111 Budapest, Hungary
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9
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Kumar P, Cruz JM, Parmananda P. Pattern selection and regulation using noise in a liquid metal. Phys Rev E 2019; 99:040201. [PMID: 31108693 DOI: 10.1103/physreve.99.040201] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2018] [Indexed: 11/07/2022]
Abstract
Electric forcing can be used to select and to regulate the shape of liquid metals. In this work, we present a transition among different patterns in a liquid mercury drop regulated by noise. A stochastic resonancelike phenomenon was observed for two different structural transitions of the liquid metal. In the first set of experiments, the transition from irregular (I) → triangular (T) → irregular (I) patterns was obtained by increasing the amplitude of biased white noise. In the second part, we observed the transition from irregular (I) → elliptical (E) → irregular (I) patterns using the same kind of noise. Periodic stochastic resonance was corroborated in our experiments by employing the cross-correlation coefficient technique.
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Affiliation(s)
- Pawan Kumar
- Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai-400 076, India
| | - J M Cruz
- 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
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10
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Taylor AF. Mechanism and Phenomenology of an Oscillating Chemical Reaction. PROGRESS IN REACTION KINETICS AND MECHANISM 2019. [DOI: 10.3184/007967402103165414] [Citation(s) in RCA: 97] [Impact Index Per Article: 19.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Chemical reactions, which are far from equilibrium, are capable of displaying oscillations in species concentrations and hence in colour, electrode potential, pH and/or temperature. The oscillations arise from the interplay between positive and negative kinetic feedback. Mechanisms for such reactions are presented, along with the rich phenomenology that these systems exhibit, from complex oscillations and chemical waves, to stationary concentration patterns. This review will focus on the Belousov-Zhabotinksy reaction but reference to other reactions will be made where appropriate.
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11
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Maoiléidigh DÓ. Multiple mechanisms for stochastic resonance are inherent to sinusoidally driven noisy Hopf oscillators. Phys Rev E 2018; 97:022226. [PMID: 29548250 DOI: 10.1103/physreve.97.022226] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2017] [Indexed: 11/07/2022]
Abstract
To ensure their sensitivity to weak periodic signals, some physical systems likely operate near a Hopf bifurcation. Many systems operating near such a bifurcation exhibit stochastic resonance, but it is unclear which mechanisms for resonance are inherent to the bifurcation. To address this question, we study the sinusoidally forced dynamics of noisy supercritical and subcritical Hopf oscillators. We find four qualitatively different mechanisms for stochastic resonance and determine the conditions for each type of resonance.
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Affiliation(s)
- Dáibhid Ó Maoiléidigh
- Department of Otolaryngology-Head and Neck Surgery, Stanford University School of Medicine, Stanford, CA 94305, USA and Laboratory of Sensory Neuroscience, The Rockefeller University, New York, NY 10065, USA
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12
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Srivastava R, Dueñas-Díez M, Pérez-Mercader J. Feed rate noise modulates autocatalysis and shapes the oscillations of the Belousov–Zhabotinsky reaction in a continuous stirred tank reactor. REACT CHEM ENG 2018. [DOI: 10.1039/c7re00196g] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Noise applied to a specific reactant feed rate directs the Belousov–Zhabotinsky reaction into specific pathways and results in noise-controlled oscillation shapes and features.
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Affiliation(s)
- Rohit Srivastava
- Department of Earth and Planetary Sciences and Origins of Life Initiative
- Harvard University
- Cambridge
- USA
| | - Marta Dueñas-Díez
- Department of Earth and Planetary Sciences and Origins of Life Initiative
- Harvard University
- Cambridge
- USA
- Repsol Technology Centre
| | - Juan Pérez-Mercader
- Department of Earth and Planetary Sciences and Origins of Life Initiative
- Harvard University
- Cambridge
- USA
- Santa Fe Institute
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13
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Voorsluijs V, Kevrekidis IG, De Decker Y. Nonlinear behavior and fluctuation-induced dynamics in the photosensitive Belousov-Zhabotinsky reaction. Phys Chem Chem Phys 2017; 19:22528-22537. [PMID: 28809962 DOI: 10.1039/c7cp03260a] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
The photosensitive Belousov-Zhabotinsky (pBZ) reaction has been used extensively to study the properties of chemical oscillators. In particular, recent experiments revealed the existence of complex spatiotemporal dynamics for systems consisting of coupled micelles (V < 10-21 L) or droplets (V ≈ [10-8-10-11] L) in which the pBZ reaction takes place. These results have been mostly understood in terms of reaction-diffusion models. However, in view of the small size of the droplets and micelles, large fluctuations of concentrations are to be expected. In this work, we investigate the role of fluctuations on the dynamics of a single droplet with stochastic simulations of an extension of the Field-Körös-Noyes (FKN) model taking into account the photosensitivity. The birhythmicity and chaotic behaviors predicted by the FKN model in the absence of fluctuations become transient or intermittent regimes whose lifetime decreases with the size of the droplet. Simple oscillations are more robust and can be observed even in small systems (V > 10-12 L), which justifies the use of deterministic models in microfluidic systems of coupled oscillators. The simulations also reveal that fluctuations strongly affect the efficiency of inhibition by light, which is often used to control the kinetics of these systems: oscillations are found for parameter values for which they are supposed to be quenched according to deterministic predictions.
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Affiliation(s)
- Valérie Voorsluijs
- Center for Nonlinear Phenomena and Complex Systems (CENOLI), Université libre de Bruxelles (ULB), Campus Plaine, C.P. 231, B-1050 Brussels, Belgium.
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14
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Davtyan A, Platkov M, Gruebele M, Papoian GA. Stochastic Resonance in Protein Folding Dynamics. Chemphyschem 2016; 17:1305-13. [PMID: 26992148 DOI: 10.1002/cphc.201501125] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2015] [Indexed: 11/09/2022]
Abstract
Although protein folding reactions are usually studied under static external conditions, it is likely that proteins fold in a locally fluctuating cellular environment in vivo. To mimic such behavior in in vitro experiments, the local temperature of the solvent can be modulated either harmonically or using correlated noise. In this study, coarse-grained molecular simulations are used to investigate these possibilities, and it is found that both periodic and correlated random fluctuations of the environment can indeed accelerate folding kinetics if the characteristic frequencies of the applied fluctuations are commensurate with the internal timescale of the folding reaction; this is consistent with the phenomenon of stochastic resonance observed in many other condensed-matter processes. To test this theoretical prediction, the folding dynamics of phosphoglycerate kinase under harmonic temperature fluctuations are experimentally probed using Förster resonance energy transfer fluorescence measurements. To analyze these experiments, a combination of theoretical approaches is developed, including stochastic simulations of folding kinetics and an analytical mean-field kinetic theory. The experimental observations are consistent with the theoretical predictions of stochastic resonance in phosphoglycerate kinase folding. When combined with an alternative experiment on the protein VlsE using a power spectrum analysis, elaborated in Dave et al., ChemPhysChem 2016, 10.1002/cphc.201501041, the overall data overwhelmingly point to the experimental confirmation of stochastic resonance in protein folding dynamics.
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Affiliation(s)
- Aram Davtyan
- Department of Chemistry and Institute for Biophysical Dynamics, Computation Institute, James Franck Institute, University of Chicago, Chicago, Illinois, 60637, USA
| | - Max Platkov
- Department of Physics, Ariel University, Ariel, 40770, Israel
| | - Martin Gruebele
- Department of Chemistry and Physics and, Center for Biophysics and Computational Biology, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
| | - Garegin A Papoian
- Department of Chemistry and Biochemistry and, Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA.
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15
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Zubarev DY, Pachón LA. Sustainability of Transient Kinetic Regimes and Origins of Death. Sci Rep 2016; 6:20562. [PMID: 26853459 PMCID: PMC4744936 DOI: 10.1038/srep20562] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2015] [Accepted: 01/06/2016] [Indexed: 11/12/2022] Open
Abstract
It is generally recognized that a distinguishing feature of life is its peculiar capability to avoid equilibration. The origin of this capability and its evolution along the timeline of abiogenesis is not yet understood. We propose to study an analog of this phenomenon that could emerge in non-biological systems. To this end, we introduce the concept of sustainability of transient kinetic regimes. This concept is illustrated via investigation of cooperative effects in an extended system of compartmentalized chemical oscillators under batch and semi-batch conditions. The computational study of a model system shows robust enhancement of lifetimes of the decaying oscillations which translates into the evolution of the survival function of the transient non-equilibrium regime. This model does not rely on any form of replication. Rather, it explores the role of a structured effective environment as a contributor to the system-bath interactions that define non-equilibrium regimes. We implicate the noise produced by the effective environment of a compartmentalized oscillator as the cause of the lifetime extension.
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Affiliation(s)
- Dmitry Yu Zubarev
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138 USA
| | - Leonardo A Pachón
- Grupo de Física Atómica y Molecular, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA; Calle 70 No. 52-21, Medellín, Colombia
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16
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Dave K, Davtyan A, Papoian GA, Gruebele M, Platkov M. Environmental Fluctuations and Stochastic Resonance in Protein Folding. Chemphyschem 2016; 17:1341-8. [PMID: 26711088 DOI: 10.1002/cphc.201501041] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2015] [Indexed: 11/07/2022]
Abstract
Stochastic resonance is a mechanism whereby a weak signal becomes detectable through the addition of noise. It is common in many macroscopic biological phenomena, but here we ask whether it can be observed in a microscopic biological phenomenon, protein folding. We investigate the folding kinetics of the protein VlsE, with a folding relaxation time of about 0.7 seconds at 38 °C in vitro. First we show that the VlsE unfolding/refolding reaction can be driven by a periodic thermal excitation above the reaction threshold. We detect the reaction by fluorescence from FRET labels on VlSE and show that accurate rate coefficients and activation barriers can be obtained from modulated kinetics. Then we weaken the periodic temperature modulation below the reaction threshold, and show that addition of artificial thermal noise speeds up the reaction from an undetectable to a detectable rate. We observe a maximum in the recovered signal as a function of thermal noise, a stochastic resonance. Simulation of a small model-protein, analysis in an accompanying theory paper, and our experimental result here all show that correlated noise is a physically and chemically plausible mechanism by which cells could modulate biomolecular dynamics during threshold processes such as signaling.
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Affiliation(s)
- Kapil Dave
- Center for Biophysics and Quantitative Biology, University of Illinois, Urbana, IL, 61801, USA
| | - Aram Davtyan
- Department of Chemistry and Institute for Biophysical Dynamics, Computation Institute, James Franck Institute, University of Chicago, Chicago, IL, 60637, USA
| | - Garegin A Papoian
- Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA
| | - Martin Gruebele
- Center for Biophysics and Quantitative Biology, University of Illinois, Urbana, IL, 61801, USA. .,Departments of Chemistry and Physics, University of Illinois, Urbana, IL, 61801, USA.
| | - Max Platkov
- Department of Physics, Ariel University, Ariel, 40770, Israel
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17
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Barroo C, De Decker Y, Visart de Bocarmé T, Gaspard P. Fluctuating Dynamics of Nanoscale Chemical Oscillations: Theory and Experiments. J Phys Chem Lett 2015; 6:2189-2193. [PMID: 26266590 DOI: 10.1021/acs.jpclett.5b00850] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Chemical oscillations are observed in a variety of reactive systems, including biological cells, for the functionality of which they play a central role. However, at such scales, molecular fluctuations are expected to endanger the regularity of these behaviors. The question of the mechanism by which robust oscillations can nevertheless emerge is still open. In this work, we report on the experimental investigation of nanoscale chemical oscillations observed during the NO2 + H2 reaction on platinum, using field electron microscopy. We show that the correlation time and the variance of the period of oscillations are connected by a universal constraint, as predicted theoretically for systems subjected to a phenomenon called phase diffusion. These results open the way to a better understanding, modeling, and control of nanoscale oscillators.
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Affiliation(s)
- Cédric Barroo
- ‡Chemical Physics of Materials - Catalysis and Tribology, Université libre de Bruxelles (ULB), Campus Plaine, Code Postal 243, B-1050 Brussels, Belgium
| | | | - Thierry Visart de Bocarmé
- ‡Chemical Physics of Materials - Catalysis and Tribology, Université libre de Bruxelles (ULB), Campus Plaine, Code Postal 243, B-1050 Brussels, Belgium
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18
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Shaw PK, Saha D, Ghosh S, Janaki MS, Iyengar ANS. Intrinsic noise induced coherence resonance in a glow discharge plasma. CHAOS (WOODBURY, N.Y.) 2015; 25:043101. [PMID: 25933649 DOI: 10.1063/1.4916772] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Experimental evidence of intrinsic noise induced coherence resonance in a glow discharge plasma is being reported. Initially the system is started at a discharge voltage (DV) where it exhibited fixed point dynamics, and then with the subsequent increase in the DV spikes were excited which were few in number and with further increase of DV the number of spikes as well as their regularity increased. The regularity in the interspike interval of the spikes is estimated using normalized variance. Coherence resonance was determined using normalized variance curve and also corroborated by Hurst exponent and power spectrum plots. We show that the regularity of the excitable spikes in the floating potential fluctuation increases with the increase in the DV, up to a particular value of DV. Using a Wiener filter, we separated the noise component which was observed to increase with DV and hence conjectured that noise can play an important role in the generation of the coherence resonance. From an anharmonic oscillator equation describing ion acoustic oscillations, we have been able to obtain a FitzHugh-Nagumo like model which has been used to understand the excitable dynamics of glow discharge plasma in the presence of noise. The numerical results agree quite well with the experimental results.
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Affiliation(s)
- Pankaj Kumar Shaw
- Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064, India
| | - Debajyoti Saha
- Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064, India
| | - Sabuj Ghosh
- Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064, India
| | - M S Janaki
- Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064, India
| | - A N Sekar Iyengar
- Plasma Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Kolkata 700064, India
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Simakov DSA, Pérez-Mercader J. Noise induced oscillations and coherence resonance in a generic model of the nonisothermal chemical oscillator. Sci Rep 2014; 3:2404. [PMID: 23929212 PMCID: PMC3738947 DOI: 10.1038/srep02404] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2013] [Accepted: 07/25/2013] [Indexed: 01/26/2023] Open
Abstract
Oscillating chemical reactions are common in biological systems and they also occur in artificial non-biological systems. Generally, these reactions are subject to random fluctuations in environmental conditions which translate into fluctuations in the values of physical variables, for example, temperature. We formulate a mathematical model for a nonisothermal minimal chemical oscillator containing a single negative feedback loop and study numerically the effects of stochastic fluctuations in temperature in the absence of any deterministic limit cycle or periodic forcing. We show that noise in temperature can induce sustained limit cycle oscillations with a relatively narrow frequency distribution and some characteristic frequency. These properties differ significantly depending on the noise correlation. Here, we have explored white and colored (correlated) noise. A plot of the characteristic frequency of the noise induced oscillations as a function of the correlation exponent shows a maximum, therefore indicating the existence of autonomous stochastic resonance, i.e. coherence resonance.
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Affiliation(s)
- David S A Simakov
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, United States of America.
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20
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Simakov DSA, Pérez-Mercader J. Effect of Noise Correlation on Noise-Induced Oscillation Frequency in the Photosensitive Belousov–Zhabotinsky Reaction in a Continuous Stirred Tank Reactor. J Phys Chem A 2013; 117:13999-4005. [DOI: 10.1021/jp409033j] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Affiliation(s)
- David S. A. Simakov
- Department
of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Juan Pérez-Mercader
- Department
of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
- Santa Fe Institute, Santa Fe, New Mexico 87501, United States
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21
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He M, Xu W, Sun Z, Jia W. Stochastic resonance quantified by statistical complexity measures in a bistable system subject to colored noise. ACTA ACUST UNITED AC 2013. [DOI: 10.1007/s40435-013-0023-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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22
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Li JC, Mei DC. Reverse resonance in stock prices of financial system with periodic information. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:012811. [PMID: 23944522 DOI: 10.1103/physreve.88.012811] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2013] [Revised: 06/06/2013] [Indexed: 06/02/2023]
Abstract
We investigate the stochastic resonance of the stock prices in a finance system with the Heston model. The extrinsic and intrinsic periodic information are introduced into the stochastic differential equations of the Heston model for stock price by focusing on the signal power amplification (SPA). We find that for both cases of extrinsic and intrinsic periodic information a phenomenon of reverse resonance emerges in the behaviors of SPA as a function of the system and external driving parameters. Moreover, in both cases, a phenomenon of double reverse resonance is observed in the behavior of SPA versus the amplitude of volatility fluctuations, by increasing the cross correlation between the noise sources in the Heston model.
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Affiliation(s)
- Jiang-Cheng Li
- Department of Physics, Yunnan University, Kunming, 650091, People's Republic of China
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23
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Das K, Sahoo P, Murali N. Studies on oscillating chemical reaction in Cu(II)-catalyzed thiocyanate-hydrogen peroxide-NaOH system using pulsating sensor. INT J CHEM KINET 2012. [DOI: 10.1002/kin.20738] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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24
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Abstract
System coordination for a system with interaction of two pathways is investigated. Sufficient conditions for guaranteeing system coordination subject to any type, amplitude or period of external forcing are analytically derived. Effects of a pathway operating in the opposite direction on system coordination are examined in detail, and it is revealed that the pathway may enhance or restrict system coordination, depending on the values of kinetic parameters. It is concluded that increasing the complexity of enzymatic network by introducing interaction of pathways does not necessarily enhance system coordination. Numerical results using rectangular and sinusoidal forcing support the analytical results, and they quantitatively show how the system with interaction of two pathways maintain its coordination. When the sufficient conditions are satisfied, the system always develops to a finite stable (time-dependent) state under the forcing of any type, amplitude or period. When not, system coordination depends quantitatively on parameter values and the type, amplitude or period of external forcing. When two parameters are forced simultaneously, an additional factor, namely phase shifts between two forced parameters, also affects system coordination. It is shown that, unless the sufficient coordination conditions are maintained, external forcing may induce 'loss of coordination', resulting in the system having no biological functioning. The implications of the results for understanding biochemical coordination and for assessing possible consequences of modulating biochemical systems are discussed.
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Affiliation(s)
- JUNLI LIU
- Soil-Plant Dynamics Unit and Centre for Nonlinear Systems in Biology, Scottish Crop Research Institute, Dundee, DD2 5DA, UK
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25
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Huh JH. Noise-induced threshold shift and pattern formation in electroconvection by controlling characteristic time scales. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:025302. [PMID: 21929051 DOI: 10.1103/physreve.84.025302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2011] [Revised: 07/19/2011] [Indexed: 05/31/2023]
Abstract
We report external noise-induced threshold shift and pattern formation in ac-driven electroconvection (EC) in nematic liquid crystals. We investigate the noise intensity dependence of the threshold and determine the relationship f(c)(*)=hf(cd)(a) (α ∼ 1.4, h ∼ 0.1) between the characteristic cutoff frequency (f(c)(*)) of the noise and the characteristic ac frequency (f(cd)) of EC. For f(c)>f(c)(*), the noise contributes to stabilizing EC (i.e., upward threshold shift), whereas for f(c)<f(c)(*), it contributes to destabilizing EC (i.e., downward threshold shift). For f(c)=f(c)(*), the noise makes no contribution to the threshold shift. However, the characteristic wavelength of EC strongly depends on the noise intensity but not on f(c).
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Affiliation(s)
- Jong-Hoon Huh
- Department of Mechanical Information Science and Technology, Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, Fukuoka 820-8502, Japan
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26
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27
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Kolbus A, Lemarchand A, Kawczyński AL, Nowakowski B. Coherence resonances in an excitable thermochemical system with multiple stationary states. Phys Chem Chem Phys 2010; 12:13224-31. [DOI: 10.1039/c0cp00468e] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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28
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Xiao TJ, Hou Z, Xin H. Entropy production and fluctuation theorem along a stochastic limit cycle. J Chem Phys 2008; 129:114506. [DOI: 10.1063/1.2978179] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Gong Y, Xie Y, Xu B, Ma X. Enhancement of stochastic oscillations by colored noise or internal noise in NO reduction by CO on small platinum surfaces. J Chem Phys 2008; 128:124707. [PMID: 18376960 DOI: 10.1063/1.2844812] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, based on the stochastic model of NO reduction by CO on Pt crystal surfaces and taking Gaussian colored noise as external fluctuations of the NO partial pressure, we study the effect of the colored noise on the internal noise-induced stochastic oscillations (INSOs) and the effect of internal noise on the colored noise-induced stochastic oscillations (CNSOs). It is found that the INSO can be enhanced by the colored noise with appropriate correlation time or noise strength and, interestingly, the CNSO can be enhanced by the internal noise as well and, moreover, the enhanced CNSO can reach the best oscillatory states repetitively via proper internal noises. This effect of the internal noise is different from its effect on the stochastic oscillations induced by the external Gaussian white noise, which probably results from the interaction of the correlated colored noise and the internal noise.
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Affiliation(s)
- Yubing Gong
- School of Physics and Electronic Engineering, Ludong University, Yantai Shandong 264025, People's Republic of China.
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30
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Jüngling T, Benner H, Stemler T, Just W. Noise-free stochastic resonance at an interior crisis. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:036216. [PMID: 18517494 DOI: 10.1103/physreve.77.036216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2007] [Indexed: 05/26/2023]
Abstract
We report on the observation of noise-free stochastic resonance in an externally driven diode resonator close to an interior crisis. At sufficiently high excitation amplitudes the diode resonator shows a strange attractor which after the collision with an unstable period-three orbit exhibits crisis-induced intermittency. In the intermittency regime the system jumps between the previously stable chaotic attractor and the phase space region which has been made accessible by the crisis. This random process can be used to amplify a weak periodic signal through the mechanism of stochastic resonance. In contrast to conventional stochastic resonance no external noise is needed. The chaotic intrinsic dynamics plays the role of the stochastic forcing. Our data obtained from the diode resonator are compared with numerical simulations of the logistic map where a similar crisis-induced intermittency is observed.
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Affiliation(s)
- Thomas Jüngling
- Institute for Solid State Physics, Darmstadt University of Technology, Darmstadt, Germany.
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31
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Okano T, Kitagawa A, Miyakawa K. Array-enhanced coherence resonance and phase synchronization in a two-dimensional array of excitable chemical oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:046201. [PMID: 17995076 DOI: 10.1103/physreve.76.046201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2007] [Indexed: 05/17/2023]
Abstract
We investigate the spatiotemporal dynamics in a two-dimensional array of excitable elements subjected to independent external noise, where elements are prepared by localizing the Belousov-Zhabotinsky reaction in a gel matrix. We experimentally demonstrate that the coherence of noise-induced firings is improved with increasing the array size, i.e., the occurrence of array-enhanced coherence resonance. Furthermore, it is found that synchronization among oscillators which are barely coupled can be achieved via coherence resonance. Experimental observations are approximately reproduced in a numerical simulation with a forced Oregonator reaction-diffusion model.
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Affiliation(s)
- Taiji Okano
- Department of Applied Physics, Fukuoka University, Fukuoka 814-0180, Japan
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32
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Yoda M, Ushikubo T, Inoue W, Sasai M. Roles of noise in single and coupled multiple genetic oscillators. J Chem Phys 2007; 126:115101. [PMID: 17381233 DOI: 10.1063/1.2539037] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The noisy fluctuation of chemical reactions should profoundly affect the oscillatory dynamics of gene circuit. In this paper a prototypical genetic oscillator, repressilator, is numerically simulated to analyze effects of noise on oscillatory dynamics. The oscillation is coherent when the protein number and the rate of the DNA state alteration are within appropriate ranges, showing the phenomenon of coherence resonance. Stochastic fluctuation not only disturbs the coherent oscillation in a chaotic way but also destabilizes the stationary state to make the oscillation relatively stable. Bursting in translation, which is a source of intense stochastic fluctuation in protein numbers, suppresses the destructive effects of the finite leakage rate of protein production and thus plays a constructive role for the persistent oscillation. When multiple repressilators are coupled to each other, the cooperative interactions among repressilators enhance the coherence in oscillation but the dephasing fluctuation among multiple repressilators induces the amplitude fluctuation in the collective oscillation.
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Affiliation(s)
- Mitsumasa Yoda
- Department of Computational Science and Engineering, Nagoya University, Nagoya 464-8603, Japan
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33
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Yi M, Jia Y, Liu Q, Li J, Zhu C. Enhancement of internal-noise coherence resonance by modulation of external noise in a circadian oscillator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:041923. [PMID: 16711852 DOI: 10.1103/physreve.73.041923] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2006] [Indexed: 05/09/2023]
Abstract
A circadian oscillator driven by external noise and internal noise has been studied by use of the chemical Langevin equation method. When the system is near a Hopf bifurcation and driven by internal noise only, it is found that the coherence resonance phenomenon can be induced by the internal noise. When the system is simultaneously driven by internal and external noise, it is found that external-noise coherence resonance can be suppressed by internal noise, while internal-noise coherence resonance can be enhanced by modulation of the external noise intensity in a certain range of noise intensity. Another interesting result is that the external noise can regulate the optimal system size when the internal-noise coherence resonance occurs.
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Affiliation(s)
- Ming Yi
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, China
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34
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35
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Yoshimoto M, Nishikanbara M, Nomoto M, Kurosawa S. Dynamical behavior of lipid bilayer membranes for taste substances under random membrane-potential fluctuations. Biophys Chem 2005; 118:1-6. [PMID: 15996809 DOI: 10.1016/j.bpc.2005.06.008] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2005] [Revised: 06/16/2005] [Accepted: 06/16/2005] [Indexed: 11/22/2022]
Abstract
The dynamical behavior of the lipid bilayer membranes was experimentally studied under superposition of random or periodic membrane-potential fluctuations. The analysis of the mutual information has revealed that, in less than 10 Hz of random fluctuations, each of the time series of the mutual information of the transmembrane current for the five chemical substances (taste substances) has its inherent pattern, but not in a periodic fluctuation. On the other hand, the analysis of the power spectrum of the frequency could not distinguish those five basic taste substances in both random and periodic fluctuations. We provide the new detection idea of chemical substances by random fluctuations.
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Affiliation(s)
- Minoru Yoshimoto
- Department of Bioengineering, Faculty of Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan.
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36
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Yang L, Jia Y. Effects of patch temperature on spontaneous action potential train due to channel fluctuations: Coherence resonance. Biosystems 2005; 81:267-80. [PMID: 15982802 DOI: 10.1016/j.biosystems.2005.05.004] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2004] [Revised: 05/10/2005] [Accepted: 05/10/2005] [Indexed: 11/23/2022]
Abstract
Based on the Hodgkin-Huxley (HH) model, the effects of patch temperature as a control parameter on the spontaneous action potentials for finite size of membrane patch are studied. With increasing patch temperature, it is found that the mean open rates of sodium and potassium channels of the HH neuron are decreased, and the mean duration of spikes of membrane potential is also decreased, which are qualitatively consistent with previous experimental results of single ion channel. Under moderate patch size, the mean interspike interval of membrane potential first decreases, reaches a minimum, and then increases with increasing patch temperature. It is shown that for both low and high temperatures, the channels fluctuation-induced spontaneous action potentials appear to be rather irregular, while for moderate patch temperature, relatively coherent oscillations observed. By defining a measure parameter beta, we show that there is a maximal region for the measure beta in the patch temperature and patch size parameter plane where the coherence resonance phenomena are very remarkable, and the characteristic correlation time of the output also confirm our result.
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Affiliation(s)
- Lijian Yang
- Department of Physics and Institute of Biophysics, Central China Normal University, Wuhan 430079, PR China
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37
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von Haeften B, Izús G, Wio HS. System size stochastic resonance: general nonequilibrium potential framework. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:021101. [PMID: 16196540 DOI: 10.1103/physreve.72.021101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/09/2005] [Indexed: 05/04/2023]
Abstract
We study the phenomenon of system size stochastic resonance within the nonequilibrium potential framework. We analyze three different cases of spatially extended systems, exploiting the knowledge of their nonequilibrium potential, showing that through the analysis of that potential we can obtain a clear physical interpretation of this phenomenon in wide classes of extended systems. Depending on the characteristics of the system, the phenomenon is associated with a breaking of the symmetry of the nonequilibrium potential or a deepening of the potential minima yielding an effective scaling of the noise intensity with the system size.
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Affiliation(s)
- B von Haeften
- Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600 Mar del Plata, Argentine
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38
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Explicit internal signal stochastic resonance and mechanic of noise-resistance in a chemical oscillator. Comput Chem Eng 2005. [DOI: 10.1016/j.compchemeng.2005.03.006] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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39
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Miyakawa K, Okano T, Tanaka T. Noise-induced spatiotemporal dynamics in a linear array of excitable chemical oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:066202. [PMID: 16089844 DOI: 10.1103/physreve.71.066202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2005] [Indexed: 05/03/2023]
Abstract
The effects of additive noise on spatiotemporal dynamics are investigated in a one-dimensional array of excitable elements in which the Belousov-Zhabotinsky reaction is localized. At the appropriate separation between adjacent elements, we find that the resonance effect becomes larger for the element being more apart from the first element when only the first element is subjected to the external noise. This phenomenon is a sort of array-enhanced resonance. Furthermore, we find that phase locking between the first element and the other elements is induced via coherence resonance of the first element. Experimental observations are approximately reproduced in a numerical simulation with a forced Oregonator reaction-diffusion model.
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Affiliation(s)
- Kenji Miyakawa
- Department of Applied Physics, Fukuoka University, Fukuoka 814-0180, Japan
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40
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Mangioni SE, Wio HS. Interplay between noise and boundary conditions in pattern formation in adsorbed substances. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:056203. [PMID: 16089630 DOI: 10.1103/physreve.71.056203] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2004] [Indexed: 05/03/2023]
Abstract
We have studied the interplay between noise and boundary conditions on the possibility of noise induced pattern formation. With this aim, we have exploited a deterministic model for pattern formation in adsorbed substances--including the effect of lateral interactions--used to describe the phenomenon of adsorption in surfaces, where a multiplicative noise fulfilling a fluctuation-dissipation relation was added. We have found solutions for different boundary conditions, particularly corresponding to two stable and one unstable patterns, where one of the stable and the unstable one, are purely induced by the multiplicative noise. In the case of albedo boundary conditions we have found a transition from monostable to a noise induced bistable behavior as the albedo parameter is varied.
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Affiliation(s)
- Sergio E Mangioni
- Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600 Mar del Plata, Argentina
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41
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Zhao J, Chen Y, Wang J. Transient complex oscillations in a closed chemical system with coupled autocatalysis. J Chem Phys 2005; 122:114514. [PMID: 15836236 DOI: 10.1063/1.1877112] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this study, hydroquinone was introduced to the classic Belousov-Zhabotinsky (BZ) reaction to build up coupled autocatalytic feedbacks. Various complex dynamical behaviors including successive period-adding bifurcations, irregular oscillations, and frequency modulations were observed in the coupled reaction system. Not only the complexity of oscillations but also the time period during which complex oscillations persist were found to depend greatly on the initial concentration of hydroquinone, which was expected to manifest the coupling strength in the studied system. Dependence of the observed transient complex oscillations on concentrations of ferroin, sulfuric acid, bromate, and malonic acid was also characterized systematically. Numerical simulations with a modified BZ model via incorporating reactions involving hydroquinone and products of hydroquinone qualitatively reproduced the influence of hydroquinone seen in experiments.
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Affiliation(s)
- Jinpei Zhao
- Department of Chemistry and Biochemistry, The University of Windsor, Ontario, Canada
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42
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Alcor D, Allemand JF, Cogné-Laage E, Croquette V, Ferrage F, Jullien L, Kononov A, Lemarchand A. Stochastic Resonance to Control Diffusive Motion in Chemistry. J Phys Chem B 2004; 109:1318-28. [PMID: 16851097 DOI: 10.1021/jp0468307] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This paper reports on a novel procedure to tune the effective diffusion coefficient of a field-sensitive reactant in the presence of a periodic external field. We investigate the motion of two negatively charged azo dyes interacting with alpha-cyclodextrin (alpha-CD) upon action of a periodic square wave electrical field. We show that the dyes exhibit an effective diffusion coefficient D(eff) that depends on the rate constants for dye complexation within alpha-CD, the period and the amplitude of the field. UV-vis absorption, gradient field (1)H NMR, and fluorescence correlation spectroscopy (FCS) after two photon excitation are used to evidence that D(eff) may be increased far beyond its intrinsic value when specific relations interpreted as a stochastic resonance are fulfilled. The present results may find useful applications in chemical kinetics as well as for molecular sorting.
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Affiliation(s)
- Damien Alcor
- Ecole Normale Supérieure, Département de Chimie, C.N.R.S. U.M.R. 8640, 24, rue Lhomond, 75231 Paris Cedex 05, France
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43
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Tatara E, Birol I, Teymour F, Çınar A. Static and Dynamic Behavior of Autocatalytic Replicators in Reactor Networks. Ind Eng Chem Res 2004. [DOI: 10.1021/ie030802d] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Eric Tatara
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
| | - Inanc Birol
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
| | - Fouad Teymour
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
| | - Ali Çınar
- Department of Chemical and Environmental Engineering, Illinois Institute of Technology, 10 West 33rd Street, Chicago, Illinois 60616
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Abstract
This paper reviews recent developments in the field of nonlinear chemical kinetics. Five topics are dealt with: (a) new approaches to complex reaction mechanisms, stoichiometric network analysis, classification of chemical oscillators and formulation of their mechanisms by deduction from experiments, and correlation metric construction of reaction pathways from measurements; (b) thermodynamic and stochastic theory of nonequilibrium processes, the eikonal approximation, the evaluation of stochastic potentials, experimental tests of the thermodynamic and stochastic theory of relative stability, and fluctuation-dissipation relations in nonequilibrium chemical systems; (c) chemical kinetics and cellular automata and lattice gas automata; (d) theoretical approaches and experimental studies of stochastic resonance in chemical kinetics; and (e) rate processes in disordered systems, stochastic Liouville equations, stretched exponential relaxation in disordered systems, and universality classes for rate processes in systems with static or dynamic disorder.
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Affiliation(s)
- J Ross
- Department of Chemistry, Stanford University, Stanford, CA 94305-5080, USA.
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45
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Synchronized and intermittent oscillations observed in a sub Belousov–Zhabotinsky reactor under continuous mass flow from a main reactor. Chem Phys Lett 2004. [DOI: 10.1016/j.cplett.2004.02.027] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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von Haeften B, Izús G, Mangioni S, Sánchez AD, Wio HS. Stochastic resonance between dissipative structures in a bistable noise-sustained dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:021107. [PMID: 14995427 DOI: 10.1103/physreve.69.021107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2003] [Indexed: 05/24/2023]
Abstract
We study an extended system that without noise shows a monostable dynamics, but when submitted to an adequate multiplicative noise, an effective bistable dynamics arises. The stochastic resonance between the attractors of the noise-sustained dynamics is investigated theoretically in terms of a two-state approximation. The knowledge of the exact nonequilibrium potential allows us to obtain the output signal-to-noise ratio. Its maximum is predicted in the symmetric case for which both attractors have the same nonequilibrium potential value.
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Affiliation(s)
- B von Haeften
- Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata, Deán Funes 3350, 7600 Mar del Plata, Argentina
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Kiss IZ, Hudson JL, Escalera Santos GJ, Parmananda P. Experiments on coherence resonance: noisy precursors to Hopf bifurcations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:035201. [PMID: 12689121 DOI: 10.1103/physreve.67.035201] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2002] [Indexed: 05/24/2023]
Abstract
Experimental and numerical evidence of coherence resonance in an electrochemical system is reported. External noise with a Gaussian distribution is superimposed on the system when the anodic current is exhibiting stationary (fixed point) dynamics below a supercritical Hopf bifurcation. The amplitude of the added stochastic perturbations is increased monotonically and the induced oscillatory behavior is analyzed. It is observed, both in experiments and in simulations, that the regularity of the noise induced current oscillations reaches a maximum value for an optimum noise level. This is indicative of coherence resonance and can be explained with a mechanism based on noisy precursors to a Hopf bifurcation.
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Affiliation(s)
- István Z Kiss
- Department of Chemical Engineering, Thornton Hall, University of Virginia, Charlottesville 22903-2442, USA
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Miyakawa K, Isikawa H. Experimental observation of coherence resonance in an excitable chemical reaction system. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:046204. [PMID: 12443296 DOI: 10.1103/physreve.66.046204] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2002] [Indexed: 05/24/2023]
Abstract
Dynamics of an excitable Belousov-Zabotinsky reaction system under an external noise are investigated using cation exchange beads loaded with the cationic catalyst. When a noise amplitude is increased above a certain value, an oscillatory state appears. It is shown that the coherence of these noise-excited oscillations is maximal for a suitable value of the noise amplitude. This phenomenon is characterized by using various statistical measures, such as the signal-to-noise ratio in the power spectrum, the correlation time of the noise-excited oscillation, and the standard deviation of time intervals between successive firing events. We find the experimental evidence that the period of coherent oscillation is determined by a characteristic time scale of the system.
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Affiliation(s)
- Kenji Miyakawa
- Department of Applied Physics, Fukuoka University, Japan
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Kortlüke O, Kuzovkov VN, von Niessen W. Internal spatiotemporal stochastic resonance in the presence of weak noise. PHYSICAL REVIEW E 2002; 66:036139. [PMID: 12366216 DOI: 10.1103/physreve.66.036139] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2000] [Revised: 05/30/2002] [Indexed: 11/07/2022]
Abstract
We show the existence of internal stochastic resonance in a microscopic stochastic model for the oscillating A+1 / 2B(2) reaction on a square lattice. This stochastic resonance arises directly from the elementary reaction steps of the system without any external input. The lattice gas model is investigated by means of Monte Carlo simulations. It shows oscillation phenomena and mesoscopic pattern formation. Stochastic resonance arises when homogeneous nucleation of the individual lattice site states is considered. This nucleation is modeled as a weak noise process. As a result, synchronization of the kinetic oscillations is obtained. We show that all characteristics known from the research on stochastic resonance are obtained in our model. We also show that the model explains easily several phenomena observed in the experiment. Internal stochastic resonance may thus be an internal regulation mechanism of extreme adaptability.
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Affiliation(s)
- O Kortlüke
- Institut für Physikalische und Theoretische Chemie, Technische Universität Braunschweig, Hans-Sommer-Strasse 10, Germany
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