Combined action of non-Gaussian noise and time delay on stochastic dynamical features for a metapopulation system driven by a multiplicative periodic signal

In this paper, we focus on investigating the steady state behaviors and the signal-to-noise ratio (SNR) for a stochastic metapopulation system with time delay induced by the cross-correlated multiplicative non-Gaussian noise and additive Gaussian noise. It is found by the numerical calculation that time delay, the strength of the multiplicative noise, the intensity of the additive one and the departure parameter from the Gaussian noise can all reduce greatly the stability of the biological population system and hold down the reproduction of the metapopulation, while the correlation time of the multiplicative noise and the noise correlation strength can strengthen the stability of the ecological system and facilitate the expansion of the population system. As regards the stochastic resonance effect (SR) evoked by time delay, the correlated noises and a multiplicative periodic signal, the consequence exhibits that due to the action of the noise correlation time τ, the SR effect is always enhanced. While time delay α, the departure parameter q and the noise intensity Q play mainly critical roles in weakening the SR and reducing the SNR. On different occasions, the noise correlation strength λ plays inverse roles in stimulating the SR effect. In particular, what is worth mentioning is that in the SNR-τ plots, time delay α, the noise intensities Q, M will all improve greatly the maximum of the SNR.