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Göth N, Baul U, Dzubiella J. Active responsive colloids driven by intrinsic dichotomous noise. Phys Rev E 2022; 106:064611. [PMID: 36671078 DOI: 10.1103/physreve.106.064611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 11/28/2022] [Indexed: 06/17/2023]
Abstract
We study the influence of intrinsic noise on the structure and dynamics of responsive colloids (RCs), which actively change their size and mutual interactions. The colloidal size is explicitly resolved in our RC model as an internal degree of freedom (DOF) in addition to the particle translation. A Hertzian pair potential between the RCs leads to repulsion and shrinking of the particles, resulting in an explicit responsiveness of the system to self-crowding. To render the colloids active, their size is internally driven by a dichotomous noise, randomly switching ("breathing") between growing and shrinking states with a predefined rate, as motivated by recent experiments on synthetic active colloids. The polydispersity of this dichotomous active responsive colloid (D-ARC) model can be tuned by the parameters of the noise. Utilizing stochastic computer simulations, we study crowding effects on the spatial distributions, relaxation times, and self-diffusion of dense suspensions of the D-ARCs. We find a substantial influence of the "built-in" intrinsic noise on the system's behavior, in particular, transitions from unimodal to bimodal size distributions for an increasing colloid density as well as intrinsic noise-modified diffusive translational dynamics. We conclude that controlling the noise of internal DOFs of a macromolecule or cell is a powerful tool for active colloidal materials to enable autonomous changes in the system's collective structure and dynamics towards the adaptation of macroscopic properties to external perturbations.
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Affiliation(s)
- Nils Göth
- Applied Theoretical Physics-Computational Physics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
| | - Upayan Baul
- Applied Theoretical Physics-Computational Physics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
| | - Joachim Dzubiella
- Applied Theoretical Physics-Computational Physics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, D-79104 Freiburg, Germany
- Cluster of Excellence livMatS @ FIT-Freiburg Center for Interactive Materials and Bioinspired Technologies, Albert-Ludwigs-Universität Freiburg, D-79110 Freiburg, Germany
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Mankin R, Rekker A. Effects of transient subordinators on the firing statistics of a neuron model driven by dichotomous noise. Phys Rev E 2020; 102:012103. [PMID: 32794976 DOI: 10.1103/physreve.102.012103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 06/15/2020] [Indexed: 06/11/2023]
Abstract
The behavior of a stochastic perfect integrate-and-fire (PIF) model of neurons is considered. The effect of temporally correlated random activity of synaptic inputs is modeled as a combination of an asymmetric dichotomous noise and a random operation time in the form of an inverse strictly increasing Lévy-type subordinator. Using a first-passage-time formulation, we find exact expressions for the output interspike interval (ISI) statistics. Particularly, it is shown that at some parameter regimes the ISI density exhibits a multimodal structure. Moreover, it is demonstrated that the coefficient of variation, the serial correlation coefficient, and the Fano factor display a nonmonotonic dependence on the mean input current μ, i.e., the ISI's regularity is maximized at an intermediate value of μ. The features of spike statistics, analytically revealed in our study, are compared with previously obtained results for a perfect integrate-and-fire neuron model driven by dichotomous noise (without subordination).
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Affiliation(s)
- Romi Mankin
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Astrid Rekker
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
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3
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Budini AA, McHardy I, Nizama M, Cáceres MO. Emergence of stationary multimodality under two-timescaled dichotomic noise. Phys Rev E 2020; 101:052137. [PMID: 32575231 DOI: 10.1103/physreve.101.052137] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Accepted: 05/06/2020] [Indexed: 11/07/2022]
Abstract
We study a linear Langevin dynamics driven by an additive non-Markovian symmetrical dichotomic noise. It is shown that when the statistics of the time intervals between noise transitions is characterized by two well differentiated timescales, the stationary distribution may develop multimodality (bi- and trimodality). The underlying effects that lead to a probability concentration in different points include intermittence and also a dynamical locking of realizations. Our results are supported by numerical simulations as well as by an exact treatment obtained from a Markovian embedding of the full dynamics, which leads to a third-order differential equation for the stationary distribution.
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Affiliation(s)
- Adrián A Budini
- Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Centro Atómico Bariloche, Avenida E. Bustillo Km 9.5, (8400) Bariloche, Argentina and Universidad Tecnológica Nacional (UTN-FRBA), Fanny Newbery 111, (8400) Bariloche, Argentina
| | - Isaias McHardy
- Fellowship CONICET, Centro Atómico Bariloche, 8400 Bariloche, Argentina
| | - Marco Nizama
- Departamento de Física, Universidad Nacional del Comahue and CONICET, 8300 Neuquen, Argentina
| | - Manuel O Cáceres
- Centro Atómico Bariloche, CNEA, Instituto Balseiro, Universidad Nacional de Cuyo, and CONICET, 8400 Bariloche, Argentina
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Lucas M, Newman J, Stefanovska A. Stabilization of dynamics of oscillatory systems by nonautonomous perturbation. Phys Rev E 2018; 97:042209. [PMID: 29758664 DOI: 10.1103/physreve.97.042209] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2017] [Indexed: 11/07/2022]
Abstract
Synchronization and stability under periodic oscillatory driving are well understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly varying frequency, and investigate both short-term and long-term stability properties. For a phase oscillator, we find that, counterintuitively, such variation is guaranteed to enlarge the Arnold tongue in parameter space. Using analytical and numerical methods that provide information on time-variable dynamical properties, we find that the growth of the Arnold tongue is specifically due to the growth of a region of intermittent synchronization where trajectories alternate between short-term stability and short-term neutral stability, giving rise to stability on average. We also present examples of higher-dimensional nonlinear oscillators where a similar stabilization phenomenon is numerically observed. Our findings help support the case that in general, deterministic nonautonomous perturbation is a very good candidate for stabilizing complex dynamics.
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Affiliation(s)
- Maxime Lucas
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom.,INFN and CSDC, Dipartimento di Fisica e Astronomia, Università di Firenze, 50019 Sesto Fiorentino, Firenze, Italy
| | - Julian Newman
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Aneta Stefanovska
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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5
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Mankin R, Rekker A. Response to a periodic stimulus in a perfect integrate-and-fire neuron model driven by colored noise. Phys Rev E 2016; 94:062103. [PMID: 28085436 DOI: 10.1103/physreve.94.062103] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2016] [Indexed: 06/06/2023]
Abstract
The output interspike interval statistics of a stochastic perfect integrate-and-fire neuron model driven by an additive exogenous periodic stimulus is considered. The effect of temporally correlated random activity of synaptic inputs is modeled by an additive symmetric dichotomous noise. Using a first-passage-time formulation, exact expressions for the output interspike interval density and for the serial correlation coefficient are derived in the nonsteady regime, and their dependence on input parameters (e.g., the noise correlation time and amplitude as well as the frequency of an input current) is analyzed. It is shown that an interplay of a periodic forcing and colored noise can cause a variety of nonequilibrium cooperation effects, such as sign reversals of the interspike interval correlations versus noise-switching rate as well as versus the frequency of periodic forcing, a power-law-like decay of oscillations of the serial correlation coefficients in the long-lag limit, amplification of the output signal modulation in the instantaneous firing rate of the neural response, etc. The features of spike statistics in the limits of slow and fast noises are also discussed.
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Affiliation(s)
- Romi Mankin
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Astrid Rekker
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
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Yang B, Zhang X, Zhang L, Luo MK. Collective behavior of globally coupled Langevin equations with colored noise in the presence of stochastic resonance. Phys Rev E 2016; 94:022119. [PMID: 27627258 DOI: 10.1103/physreve.94.022119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2015] [Indexed: 06/06/2023]
Abstract
The long-time collective behavior of globally coupled Langevin equations in a dichotomous fluctuating potential driven by a periodic source is investigated. By describing the collective behavior using the moments of the mean field and single-particle displacements, we study stochastic resonance and synchronization using the exact steady-state solutions and related stability criteria. Based on the simulation results and the criterion of the stationary regime, the notable differences between the stationary and nonstationary regimes are demonstrated. For the stationary regime, stochastic resonance with synchronization is discussed, and for the nonstationary regime, the volatility clustering phenomenon is observed.
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Affiliation(s)
- Bo Yang
- Department of Mathematics, Sichuan University, 610065, Chengdu, Sichuan, China
| | - Xiao Zhang
- Department of Mathematics, Sichuan University, 610065, Chengdu, Sichuan, China
| | - Lu Zhang
- Department of Mathematics, Sichuan University, 610065, Chengdu, Sichuan, China
| | - Mao-Kang Luo
- Department of Mathematics, Sichuan University, 610065, Chengdu, Sichuan, China
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Mankin R, Lumi N. Statistics of a leaky integrate-and-fire model of neurons driven by dichotomous noise. Phys Rev E 2016; 93:052143. [PMID: 27300865 DOI: 10.1103/physreve.93.052143] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2016] [Indexed: 06/06/2023]
Abstract
The behavior of a stochastic leaky integrate-and-fire model of neurons is considered. The effect of temporally correlated random neuronal input is modeled as a colored two-level (dichotomous) Markovian noise. Relying on the Riemann method, exact expressions for the output interspike interval density and for the serial correlation coefficient are derived, and their dependence on noise parameters (such as correlation time and amplitude) is analyzed. Particularly, noise-induced sign reversal and a resonancelike amplification of the kurtosis of the interspike interval distribution are established. The features of spike statistics, analytically revealed in our study, are compared with recently obtained results for a perfect integrate-and-fire neuron model.
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Affiliation(s)
- Romi Mankin
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Neeme Lumi
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
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Perez-Carrasco R, Sancho JM. Stochastic algorithms for discontinuous multiplicative white noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:032104. [PMID: 20365796 DOI: 10.1103/physreve.81.032104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2009] [Indexed: 05/29/2023]
Abstract
Stochastic differential equations with multiplicative noise need a mathematical prescription due to different interpretations of the stochastic integral. This fact implies specific algorithms to perform numerical integrations or simulations of the stochastic trajectories. Moreover, if the multiplicative noise function is not continuous then the standard algorithms cannot be used. We present an explicit algorithm to avoid this problem and we apply it to a well controlled example. Finally, we discuss on the existence of higher-order algorithms for this specific situation.
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Affiliation(s)
- R Perez-Carrasco
- Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain
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Li JH. Stochastic giant resonance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021113. [PMID: 17930012 DOI: 10.1103/physreve.76.021113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2007] [Revised: 07/04/2007] [Indexed: 05/25/2023]
Abstract
The model of an electric circuit with dichotomous resistance is investigated. It is shown that the dichotomous resistance can induce a phenomenon of stochastic giant resonance for the signal-to-noise ratio (SNR) as a function of input signal frequency. This phenomenon is a direct consequence of the existence of a zero noise power spectrum, with a nonzero signal power spectrum for the same parameters. In addition, two kinds of the usual stochastic resonance phenomena have been obtained for the SNR. One is as a function of the correlation time of the asymmetric dichotomous resistance; the other is as a function of the input signal frequency.
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Affiliation(s)
- Jing-hui Li
- Faculty of Science, P.O. Box 58, Ningbo University, Ningbo 315211, China
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Kim C, Lee EK, Hänggi P, Talkner P. Numerical method for solving stochastic differential equations with Poissonian white shot noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:011109. [PMID: 17677412 DOI: 10.1103/physreve.76.011109] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2007] [Indexed: 05/16/2023]
Abstract
We propose a numerical integration scheme to solve stochastic differential equations driven by Poissonian white shot noise. Our formula, which is based on an integral equation, which is equivalent to the stochastic differential equation, utilizes a discrete time approximation with fixed integration time step. We show that our integration formula approaches the Euler formula if the Poissonian noise approaches the Gaussian white noise. The accuracy and efficiency of the proposed algorithm are examined by studying the dynamics of an overdamped particle driven by Poissonian white shot noise in a spatially periodic potential. We find that the accuracy of the proposed algorithm only weakly depends on the parameters characterizing the Poissonian white shot noise; this holds true even if the limit of Gaussian white noise is approached.
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Affiliation(s)
- Changho Kim
- Department of Chemistry and School of Molecular Science (BK21), Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea
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Li JH, Han YX. Phenomenon of stochastic resonance caused by multiplicative asymmetric dichotomous noise. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:051115. [PMID: 17279885 DOI: 10.1103/physreve.74.051115] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2006] [Indexed: 05/13/2023]
Abstract
The exact expression of the first moment and the signal-to-noise ratio (SNR) have been calculated for a linear system subject to an external periodic field as well as a multiplicative asymmetric dichotomous noise, by using the Shapiro-Loginov formula. It has been found that the amplitude of the output signal, and the SNR, respectively, exhibit two kinds of the phenomena of stochastic resonance: one is as the functions of the parameters of the asymmetric dichotomous noise, such as the noise strength D, and the parameter k describing the asymmetric degree of the dichotomous noise; the other is as the function of the parameter of the input signal, such as the input signal frequency omega.
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Affiliation(s)
- Jing-hui Li
- Faculty of Science, Ningbo University, Ningbo 315211, China
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