Impact of colored cross-correlated non-Gaussian and Gaussian noises on stochastic resonance and stochastic stability for a metapopulation system driven by a multiplicative signal

In this paper, our aim is to investigate the steady state characteristics and the signal-to-noise ratio (SNR) for a stochastic metapopulation system including a multiplicative periodic signal caused by the terms of the colored cross-correlated multiplicative non-Gaussian noise and additive Gaussian noise. Numerical results indicate that the multiplicative noise, the additive one and the departure parameter from the Gaussian noise can all decrease the stability of the ecological population system and restrain the development of the metapopulation, while two noise correlation times and the strength of the noise correlation will enhance the stability of the biological system and promote the expansion of the population system. With regard to the stochastic resonance phenomenon (SR) induced by noise terms and a multiplicative weak periodic signal, the results illustrate that the noise correlation time τ and the strength of correlation noise λ can increase the SR effect greatly in most cases, while the intensity of the multiplicative noise Q mainly plays a part in suppressing the SR and weakening the SNR except that in the SNR-τ plot. Moreover, it is worth noting that the noise correlation time τ0 and the additive noise intensity M can play the diverse roles in enhancing or weakening the SR effect under the different system parameter conditions.