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

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 alpha and additive noise intensity D, and correlated intensity lambda 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 lambda for fixed ratio of alpha and D, the varying of alpha can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs lambda; (2) There exhibits a doubly critical phenomenon for SNR vs D and lambda, i.e., the increasing of D(or lambda) can induce the critical phenomenon for SNR with respect to lambda (or D); (3) The doubly stochastic resonance effect appears when alpha 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.