Stochastic resonance for a metapopulation system driven by multiplicative and additive colored noises

We investigate the stochastic resonance (SR) phenomenon induced by the periodic signal in a metapopulation system with colored noises. The analytical expression of signal-to-noise is derived in the adiabatic limit. By numerical calculation, the effects of the addictive noise intensity, the multiplicative noise intensity and two noise self-correlation times on SNR are respectively discussed. It shows that: (i) in the case that the addictive noise intensity M takes a small value, a SR phenomenon for the curve of SNR appears; however, when M takes a large value, SNR turns into a monotonic function on the multiplicative noise intensity Q. (ii) The resonance peaks in the plots of the multiplicative noise intensity Q versus its self-correlation time τ₁ and the addictive noise intensity M versus its self-correlation time τ₂ translate in parallel. Meanwhile, a parallel translation also appears in the plots of τ₁ versus Q and τ₂ versus M. (iii) The interactive effects between self-correlation times τ₁ and τ₂ are opposite.