Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise

Fox, Ronald F.; Gatland, I. R.; Roy, Rajarshi; Vemuri, Gautam

doi:10.1103/physreva.38.5938

Cited by 400 publications

(201 citation statements)

References 5 publications

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“…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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“…where D 1 is the intensity of the Gaussian white noise; and the color noise with the properties of [42] N 2 ðtÞ h i¼ 0; ð6Þ where D 2 and λ are the intensity and the correlation time of the color noise. The IPs and the DPs are calculated by the flux operator method,…”

Section: Theoretical Methodsmentioning

confidence: 99%

Intensity enhancement in the molecular ionization and dissociation dynamics in the presence of noise

Feng

Chu

2012

J Mol Model

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The ionization and the dissociation of the diatomic molecular ion H 2 + have been investigated within a scheme where a noise field is added to an intense infrared laser field. The results show that both the ionization and the dissociation probabilities are enhanced with the introduction of the additional noise (the Gaussian white noise or the color noise) field. Further, by tuning the noise intensity and the delay time between the laser and the noise, a stochastic resonancelike curve is observed for the ionization or the dissociation dynamics, showing the existence of an optimal noise intensity and delay time for the given laser field.

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“…For completeness, we briefly describe the method of solving PDEs of electrically driven nanowire systems [19], which we combine with the method for solving ODEs subject to colored noise [59]. We begin by writing Eq.…”

Section: Appendixmentioning

confidence: 99%

Regularization of chaos by noise in electrically driven nanowire systems

Hessari

Lai

et al. 2014

Phys. Rev. B

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The electrically driven nanowire systems are of great importance to nanoscience and engineering. Due to strong nonlinearity, chaos can arise, but in many applications it is desirable to suppress chaos. The intrinsically high-dimensional nature of the system prevents application of the conventional method of controlling chaos. Remarkably, we find that the phenomenon of coherence resonance, which has been well documented but for low-dimensional chaotic systems, can occur in the nanowire system that mathematically is described by two coupled nonlinear partial differential equations, subject to periodic driving and noise. Especially, we find that, when the nanowire is in either the weakly chaotic or the extensively chaotic regime, an optimal level of noise can significantly enhance the regularity of the oscillations. This result is robust because it holds regardless of whether noise is white or colored, and of whether the stochastic drivings in the two independent directions transverse to the nanowire are correlated or independent of each other. Noise can thus regularize chaotic oscillations through the mechanism of coherence resonance in the nanowire system. More generally, we posit that noise can provide a practical way to harness chaos in nanoscale systems.

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Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise

Abstract: The normal procedure for numerical simulation of exponentially correlated colored noise is superseded by the novel algorithm presented here. A differential algorithm is replaced by an integral algorithm which is faster, more accurate, and permits the use of longer step sizes.

Cited by 400 publications

References 5 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

Intensity enhancement in the molecular ionization and dissociation dynamics in the presence of noise

Regularization of chaos by noise in electrically driven nanowire systems

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