Stochastic resonance induced by a multiplicative periodic signal in a logistic growth model with correlated noises

Abstract

Abstract:The stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth. PACS

Stochastic resonance and stability for a time-delayed cancer growth system subjected to multiplicative and additive noises

“…For the case of a small delay time, the analytical approximation method for time-delayed stochastic systems has been developed [15], and in the case that the time delay is large, a numerical simulation method can be used [16]. Within many previous investigations, the different systems without time delay, SR phenomena induced by an additive signal or/and a multiplicative signal have been investigated [17][18][19][20]. For the case that a multiplicative signal, cross-correlated noises and a time delay were simultaneously added, Guillouzic et al [21] considered the effect of external fluctuations (noise) upon the delay differential equations.…”

Accuracy of the analytical escape rate for a cusp barrier in the overdamping regime

“…Accuracy of the Kramers formulas for the decay rate derived in [11] was studied in several articles (see, e.g., [15][16][17]). Unfortunately, sometimes the Kramers formulas were misinterpreted (see, for example, [18][19][20] and detailed discussion of this problem in [21,22]). Usually, they consider the Kramers formulas obtained for the parabolic barrier.…”