Impact of Time Delay and Cross-Correlated Gaussian Colored Noises on Dynamical Characteristics and Stochastic Resonance for a Metapopulation System

Abstract

In this paper, the regime shift behaviors between the prosperous state and the extinction state and stochastic resonance (SR) phenomenon for a metapopulation system subjected to time delay and correlated Gaussian colored noises are investigated. Through the numerical calculation of the modified potential function and the stationary probability density function (SPDF), one can make clearly the following results: Both multiplicative noise and noise correlation times can improve effectively the ecological stability and prolong the survival time of the system; while additive noise, time delay and noise correlation strength can weaken significantly the biological stability and speed up the extinction of the population. As for the signal-to-noise ratio (SNR), it is found that time delay, multiplicative noise and noise correlation strength can all impair the SR effect. Conversely, the two noise correlation times and additive noise are in favor of the improvement of the peak values of SNR. It is particularly worth mentioning that in the case of [Formula: see text], time delay [Formula: see text] and self-correlation time [Formula: see text] of the additive noise display exactly the opposite effect on the stimulation of the resonant peak in the SNR–[Formula: see text] plots.

Influence of colored cross-correlated noise on stochastic resonance for an underdamped bistable system subjected to multiplicative and additive noises

“…Moreover, in certain situation the correlation time for the cross-correlated noise between the multiplicative and additive noise may be nonzero, i.e., the cross-correlation noise can be a colored one. The influences of correlations between multiplicative and additive noise have been widely analyzed [2][3][4][5][6]. Cross-correlated sine-Wiener bounded noises-induced logical stochastic resonance [2], cross-correlated Gaussian colored noises on stochastic resonance for a metapopulation system [3], cross-correlated noises on the fluctuation behaviors of a gene transcriptional regulatory system [4], cross-correlated bounded noises induced population extinction and enhancement of stability in a population growth model [5], colored cross-correlated non-Gaussian noises on stochastic resonance and stochastic stability for a metapopulation system [6] have been investigated.…”

Stochastic and parameter analysis for an integrative cancer model

“…It is important to point out the Stochastic Resonance(SR): SR is the phenomenon where a system is enhanced by the combination of its dynamics and random fluctuations [11,12]. That is: the presence of an optimal level of noise or fluctuation can enhance, for example, the stability of the system [13][14][15][16]. SR is studied in several fields such as biology [17], chemistry [18], physics [19], etc.…”