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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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2
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Axelrod S, Brumer P. An efficient approach to the quantum dynamics and rates of processes induced by natural incoherent light. J Chem Phys 2018; 149:114104. [PMID: 30243280 DOI: 10.1063/1.5041005] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
In many important cases, the rate of excitation of a system embedded in an environment is significantly smaller than the internal system relaxation rates. An important example is that of light-induced processes under natural conditions, in which the system is excited by weak, incoherent (e.g., solar) radiation. Simulating the dynamics on the time scale of the excitation source can thus be computationally intractable. Here we describe a method for obtaining the dynamics of quantum systems without directly solving the master equation. We present an algorithm for the numerical implementation of this method and, as an example, use it to reconstruct the internal conversion dynamics of pyrazine excited by sunlight. Significantly, this approach also allows us to assess the role of quantum coherence on biological time scales, which is a topic of ongoing interest.
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Affiliation(s)
- Simon Axelrod
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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Xu P, Jin Y, Xiao S. Stochastic resonance in a delayed triple-well potential driven by correlated noises. CHAOS (WOODBURY, N.Y.) 2017; 27:113109. [PMID: 29195325 DOI: 10.1063/1.4994638] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
In this paper, we investigate stochastic resonance (SR) in a delayed triple-well potential subject to correlated noises and a harmonic signal. The stationary probability density, together with the response amplitude of the system, is obtained by using the small time delay approximation. It is found that the time delay, noise intensities, and the cross-correlation between noises can induce the occurrence of the transition. Moreover, the appropriate choice of noise intensities and time delay can improve the output of the system, enhance the SR effect, and lead to the phenomenon of noise enhanced stability. Especially, the stochastic multi-resonance phenomenon is observed when the multiplicative and additive noises are correlated. Finally, the theoretical results are well verified through numerical simulations.
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Affiliation(s)
- Pengfei Xu
- Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China
| | - Yanfei Jin
- Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China
| | - Shaomin Xiao
- Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China
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Yang XL, Senthilkumar DV, Sun ZK, Kurths J. Key role of time-delay and connection topology in shaping the dynamics of noisy genetic regulatory networks. CHAOS (WOODBURY, N.Y.) 2011; 21:047522. [PMID: 22225396 DOI: 10.1063/1.3629984] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
This paper focuses on a paced genetic regulatory small-world network with time-delayed coupling. How the dynamical behaviors including temporal resonance and spatial synchronization evolve under the influence of time-delay and connection topology is explored through numerical simulations. We reveal the phenomenon of delay-induced resonance when the network topology is fixed. For a fixed time-delay, temporal resonance is shown to be degraded by increasing the rewiring probability of the network. On the other hand, for small rewiring probability, temporal resonance can be enhanced by an appropriately tuned small delay but degraded by a large delay, while conversely, temporal resonance is always reduced by time-delay for large rewiring probability. Finally, an optimal spatial synchrony is detected by a proper combination of time-delay and connection topology.
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Affiliation(s)
- X L Yang
- College of Mathematics and Information Science, Shaanxi Normal University, Xián 710062, People's Republic of China
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FRANK TD, FRIEDRICH R, BEEK PJ. TIME SERIES ANALYSIS OF MULTIVARIATE TIME-DELAYED SYSTEMS WITH NOISE: APPLICATIONS TO LASER PHYSICS AND HUMAN MOVEMENT. STOCH DYNAM 2011. [DOI: 10.1142/s0219493705001456] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
A data analysis method is proposed to reconstruct evolution equations of stochastic systems with time-delayed feedback from experimental time series. Multivariate systems involving noise sources with arbitrary correlation times are considered.
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Affiliation(s)
- T. D. FRANK
- Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
| | - R. FRIEDRICH
- Institute for Theoretical Physics, University of Münster, Wilhelm-Klemm-Str. 9, 48149 Münster, Germany
| | - P. J. BEEK
- Faculty of Human Movement Sciences, Vrije Universiteit, Van der Boechorststraat 9, 1081 BT Amsterdam, The Netherlands
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FISCHER MARKUS, IMKELLER PETER. A TWO-STATE MODEL FOR NOISE-INDUCED RESONANCE IN BISTABLE SYSTEMS WITH DELAY. STOCH DYNAM 2011. [DOI: 10.1142/s0219493705001389] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We discuss a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise, exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one-dimensional parametrized stochastic differential equation with point delay, basic properties whereof we check. With the aim of capturing the effective dynamics and, in particular, the resonance-like behavior of the reference model, we construct a simplified or reduced model, the two-state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn can be used to characterize the phenomenon of noise-induced resonance. Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two-state model and the reference model. The resonance characteristics developed for the reduced model can thus be applied to the original model.
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Affiliation(s)
- MARKUS FISCHER
- Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
| | - PETER IMKELLER
- Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
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Olejniczak L, Panajotov K, Thienpont H, Sciamanna M, Mutig A, Hopfer F, Bimberg D. Polarization switching and polarization mode hopping in quantum dot vertical-cavity surface-emitting lasers. OPTICS EXPRESS 2011; 19:2476-2484. [PMID: 21369067 DOI: 10.1364/oe.19.002476] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
We show experimentally that polarization mode hopping in quantum dot vertical cavity surface emitting lasers (VCSELs) takes place between nonorthogonal elliptically polarized modes. In contrast to quantum well VCSELs the average dwell time decreases with injection current. This decrease is by 8 orders of magnitude: from seconds to nanoseconds and is achieved without any modifications of the VCSEL internal anisotropies. The observed scaling happens in a range of currents as wide as 8 times the threshold value.
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Affiliation(s)
- Lukasz Olejniczak
- Department of Applied Physics and Photonics, Brussels Photonics Team B-PHOT, Vrije Universiteit Brussel, 2 Pleinlaan, B-1050 Brussels, Belgium.
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Kimizuka M, Munakata T, Rosinberg ML. Stochastic dynamics of N bistable elements with global time-delayed interactions: towards an exact solution of the master equations for finite N. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:041129. [PMID: 21230260 DOI: 10.1103/physreve.82.041129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2010] [Indexed: 05/30/2023]
Abstract
We consider a network of N noisy bistable elements with global time-delayed couplings. In a two-state description, where elements are represented by Ising spins, the collective dynamics is described by an infinite hierarchy of coupled master equations which was solved at the mean-field level in the thermodynamic limit. When the number of elements is finite, as is the case in actual laser networks, an analytical description was deemed so far intractable and numerical studies seemed to be necessary. In this paper we consider the case of two interacting elements and show that a partial analytical description of the stationary state is possible if the stochastic process is time symmetric. This requires some relationship between the transition rates to be satisfied.
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Affiliation(s)
- M Kimizuka
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
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Kimizuka M, Munakata T. Stochastic dynamics in systems with unidirectional delay coupling: two-state description. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:021139. [PMID: 19792109 DOI: 10.1103/physreve.80.021139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2009] [Indexed: 05/28/2023]
Abstract
We study stochastic dynamics of two-state particles coupled unidirectionally with delay. We give exact results for the stationary distribution function p(st) and the time correlation function (TCF) when the system consists of two (N=2) and three (N=3) particles. Based on these results, effects of delay are discussed and compared with the N=1 case, studied by Tsimring and Pikovsky [Phys. Rev. Lett. 87, 250602 (2001)]. Next, we consider the general N -particle system, for which we give exact expressions for p(st) and the TCF, which are inferred based on the N=2 and N=3 solutions and then confirmed via detailed arguments. It is pointed out that the stationary state is mapped to Ising spin model with ferro(antiferro)magnetic interaction when delay feedback is positive (negative).
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Affiliation(s)
- Makoto Kimizuka
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
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Munakata T, Iwama S, Kimizuka M. Linear stochastic system with delay: energy balance and entropy production. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:031104. [PMID: 19391899 DOI: 10.1103/physreve.79.031104] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2008] [Revised: 12/17/2008] [Indexed: 05/27/2023]
Abstract
We study the energy balance in a linear stochastic dynamics with delay under the impact of an external periodic force. The linearity of the model, in combination with a response function method, enables us to perform detailed analytic calculations of each term in the energy balance equation. From this, we discuss thermodynamics and entropy production rate sigma . With use of the delay time tau and strength of the external force A0 , sigma is simply expressed as sigma=sigma_{D,1}(tau)+A_{0};{2}eta(tau) , with both sigma_{D,1}(tau) and eta(tau) positive definite. We thus conclude that even when there is no external force (A_{0}=0) , the entropy production rate sigma=sigma_{D,1}(tau) is positive, meaning that the delay force produces work, which is dissipated into a reservoir. Numerical experiments are performed to confirm theoretical results.
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Affiliation(s)
- Toyonori Munakata
- Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
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11
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Goulding D, Melnik S, Curtin D, Piwonski T, Houlihan J, Gleeson JP, Huyet G. Kramers' law for a bistable system with time-delayed noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:031128. [PMID: 17930220 DOI: 10.1103/physreve.76.031128] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2006] [Revised: 07/11/2007] [Indexed: 05/25/2023]
Abstract
We demonstrate that the classical Kramers' escape problem can be extended to describe a bistable system under the influence of noise consisting of the superposition of a white Gaussian noise with the same noise delayed by time tau . The distribution of times between two consecutive switches decays piecewise exponentially, and the switching rates for 0<t<tau and tau<t<2tau are calculated analytically using the Langevin equation. These rates are different since, for the particles remaining in one well for longer than tau, the delayed noise acquires a nonzero mean value and becomes negatively autocorrelated. To account for these effects we define an effective potential and an effective diffusion coefficient of the delayed noise.
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Affiliation(s)
- D Goulding
- Tyndall National Institute, Lee Maltings, Cork, Ireland
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12
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Borromeo M, Giusepponi S, Marchesoni F. Recycled noise rectification: an automated Maxwell's daemon. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:031121. [PMID: 17025608 DOI: 10.1103/physreve.74.031121] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2006] [Indexed: 05/12/2023]
Abstract
The one-dimensional motion of a massless Brownian particle on a symmetric periodic substrate can be rectified by reinjecting its driving noise through a realistic recycling procedure. If the recycled noise is multiplicatively coupled to the substrate, the ensuing feedback system works like a passive Maxwell's daemon, capable of inducing a net current that depends on both the delay and the autocorrelation times of the noise signals. Extensive numerical simulations show that the underlying rectification mechanism is a resonant nonlinear effect: The observed currents can be optimized for an appropriate choice of the recycling parameters with immediate application to the design of nanodevices for particle transport.
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Affiliation(s)
- M Borromeo
- Dipartimento di Fisica, Università di Perugia, I-06123 Perugia, Italy
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13
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Wu D, Zhu S. Brownian motor with time-delayed feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:051107. [PMID: 16802918 DOI: 10.1103/physreve.73.051107] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2005] [Revised: 02/27/2006] [Indexed: 05/10/2023]
Abstract
An inertial Brownian motor with time-delayed feedback driven by an unbiased time-periodic force is investigated. It is found that the mean velocity and the rectification efficiency are decreased when the noise intensity is increased. While the shape of the mean velocity and the rectification efficiency can be changed from one peak to two peaks when the time delay is increased, the symmetry in the velocity probability distribution function is broken when the delay time is increased.
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Affiliation(s)
- Dan Wu
- School of Physical Science and Technology, Suzhou University, Suzhou, Jiangsu 215006, People's Republic of China
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Piwonski T, Houlihan J, Busch T, Huyet G. Delay-induced excitability. PHYSICAL REVIEW LETTERS 2005; 95:040601. [PMID: 16090791 DOI: 10.1103/physrevlett.95.040601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2004] [Revised: 04/14/2005] [Indexed: 05/03/2023]
Abstract
We analyze the stochastic dynamics of a bistable system under the influence of time-delayed feedback. Assuming an asymmetric potential, we show the existence of a regime in which the system dynamics displays excitability by calculating the relevant residence time distributions and power spectra. Experimentally we then observe this behavior in the polarization dynamics of a vertical cavity surface emitting laser with optoelectronic feedback. Extending these observations to two-dimensional systems with diffusive coupling, we finally show numerically that delay-induced excitability can lead to the appearance of propagating wave fronts and spirals.
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Affiliation(s)
- Tomasz Piwonski
- Physics Department, National University of Ireland, University College Cork
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Frank TD. Delay Fokker-Planck equations, Novikov's theorem, and Boltzmann distributions as small delay approximations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:011112. [PMID: 16089942 DOI: 10.1103/physreve.72.011112] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2005] [Revised: 03/10/2005] [Indexed: 05/03/2023]
Abstract
We study time-delayed stochastic systems that can be described by means of so-called delay Fokker-Planck equations. Using Novikov's theorem, we first show that the theory of delay Fokker-Planck equations is on an equal footing with the theory of ordinary Fokker-Planck equations. Subsequently, we derive stationary distributions in the case of small time delays. In the case of additive noise systems, these distributions can be cast into the form of Boltzmann distributions involving effective potential functions.
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Affiliation(s)
- T D Frank
- Institute for Theoretical Physics, University of Münster, Germany
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Frank TD. Delay Fokker-Planck equations, perturbation theory, and data analysis for nonlinear stochastic systems with time delays. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:031106. [PMID: 15903405 DOI: 10.1103/physreve.71.031106] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2004] [Indexed: 05/02/2023]
Abstract
We study nonlinear stochastic systems with time-delayed feedback using the concept of delay Fokker-Planck equations introduced by Guillouzic, L'Heureux, and Longtin. We derive an analytical expression for stationary distributions using first-order perturbation theory. We demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data. In addition, we show that the Fokker-Planck perspective for stochastic systems with time delays is consistent with the so-called extended phase-space approach to time-delayed systems.
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Affiliation(s)
- T D Frank
- Institute for Theoretical Physics, University of Münster, Germany
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17
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Curtin D, Hegarty SP, Goulding D, Houlihan J, Busch T, Masoller C, Huyet G. Distribution of residence times in bistable noisy systems with time-delayed feedback. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:031103. [PMID: 15524502 DOI: 10.1103/physreve.70.031103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2004] [Indexed: 05/24/2023]
Abstract
We analyze theoretically and experimentally the residence time distribution of bistable systems in the presence of noise and time-delayed feedback. We explain various nonexponential features of the residence time distribution using a two-state model and obtain a quantitative agreement with an experiment based on a Schmitt trigger. The limitations of the two-state model are also analyzed theoretically and experimentally using a semiconductor laser with optoelectronic feedback.
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Affiliation(s)
- D Curtin
- Physics Department, National University of Ireland, University College, Cork, Ireland
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