Impact of time delays on stochastic resonance in an ecological system describing vegetation

Abstract

In this paper, we investigate the stochastic resonance phenomenon in a vegetation ecological system with time delay, at which the vegetation dynamics is assumed to be disturbed by both intrinsic and extrinsic noises. The signal-to-noise ratio is calculated when a weak periodic signal is added to the system. The impacts of time delay τ and correlation strength k between two noises on the signal-to-noise ratio are discussed, respectively. Our research results show that: (i) the increase of τ or k can enhance the stochastic resonance in the signal-to-noise ratio as a function of intrinsic noise strength α; (ii) on the contrary, the increase of τ or k can weaken the stochastic resonance in the signal-to-noise ratio as a function of extrinsic noise strength D; and (iii) the increase of τ can lead to double stochastic resonance phenomenon in the signal-to-noise ratio as a function of k.