Thermal activation by power-limited coloured noise

Jung, P.; Neiman, Alexander; Afghan, Muhammad; Nadkarni, Suhita; Ullah, Ghanim

doi:10.1088/1367-2630/7/1/017

Cited by 16 publications

(7 citation statements)

References 19 publications

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“…The noise correlation time τ c and the variance σ 2 are parameters that can be varied independently. Coloured noise generated by an Ornstein-Uhlenbeck process with this parametrization is referred to as power-limited coloured noise, since the total power of the noise (the integral over the spectral density of the process) is conserved upon varying the noise correlation time (Jung et al 2005). For the numerical generation of exponentially correlated coloured noise we use the integral algorithm proposed by Fox et al (1988), corresponding to a direct numerical generation of the conditional probability distribution of the Ornstein-Uhlenbeck process.…”

Section: (C) Two Coupled Systemsmentioning

confidence: 99%

Interplay of time-delayed feedback control and temporally correlated noise in excitable systems

Brandstetter

Dahlem

Schöll

2010

Phil. Trans. R. Soc. A.

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The interplay of time-delayed feedback and temporally correlated coloured noise in a single and two coupled excitable systems is studied in the framework of the FitzHughNagumo (FHN) model. By using coloured noise instead of white noise, the noise correlation time is introduced as an additional time scale. We show that in a single FHN system the major time scale of oscillations is strongly influenced by the noise correlation time, which in turn affects the maxima of coherence with respect to the delay time. In two coupled FHN systems, coloured noise input to one subsystem influences coherence resonance and stochastic synchronization of both subsystems. Application of delayed feedback control to the coloured noise-driven subsystem is shown to change coherence and time scales of noise-induced oscillations in both systems, and to enhance or suppress stochastic synchronization under certain conditions.

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Section: (C) Two Coupled Systemsmentioning

confidence: 99%

Interplay of time-delayed feedback control and temporally correlated noise in excitable systems

Brandstetter

Dahlem

Schöll

2010

Phil. Trans. R. Soc. A.

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“…(15). In this context we mention the studies on colored noise [66,67], which assume random fluctuations whose strength scales with the dynamical time scale τ 0 . These studies presume that τ 0 → 0 yields the white-noise fluctuations with non-vanishing variance.…”

Section: The Stochastic Center Manifold Analysismentioning

confidence: 99%

Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift–Hohenberg equation

Hutt

Longtin

Schimansky‐Geier

2008

Physica D: Nonlinear Phenomena

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“…where the parameter s 2 Z D=t is the variance of the process given by its second moment hh 2 i and t is the characteristic correlation time. Two different interpretations of the white noise limit t/0 arise depending on the parametrization of the OU noise (Jung et al 2005). In the first one, the noise intensity D is kept fixed and the effect of noise is studied as the correlation time t is changed; while in the second one, the effects induced by changes in the colour of the fluctuations are explored keeping the variance s 2 constant.…”

Section: Introductionmentioning

confidence: 99%

Coherence resonance in a chemical excitable system driven by coloured noise

Beato

Sendiña‐Nadal

Gerdes

et al. 2007

Phil. Trans. R. Soc. A.

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We investigate how the temporal correlation in excitable systems driven by external noise affects the coherence of the system's response. The coupling to the fluctuating environment is introduced via fluctuations of a bifurcation parameter that controls the local dynamics of the light-sensitive Belousov-Zhabotinsky reaction and of its numerical description, the Oregonator model. Both systems are brought from a highly incoherent regime to a coherent one by an appropriate choice of the correlation time and keeping noise variance constant. This effect has been found both for an Ornstein-Uhlenbeck process and for a dichotomous telegraph signal. In the latter case, we are able to connect the optimal correlation time, for which the system behaviour is most coherent, with a characteristic time scale of the system.

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Thermal activation by power-limited coloured noise

Cited by 16 publications

References 19 publications

Interplay of time-delayed feedback control and temporally correlated noise in excitable systems

Interplay of time-delayed feedback control and temporally correlated noise in excitable systems

Additive noise-induced Turing transitions in spatial systems with application to neural fields and the Swift–Hohenberg equation

Coherence resonance in a chemical excitable system driven by coloured noise

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