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

• We investigate stochastic resonance (SR) in a vegetation ecological system with time delay.
• Time delay and correlation strength enhance SR in SNR versus intrinsic noise strength.
• Time delay and correlation strength weaken SR in SNR versus extrinsic noise strength.
• Time delay leads to double SR in SNR versus correlation strength.

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 ττ and correlation strength kk between two noises on the signal-to-noise ratio are discussed, respectively. Our research results show that: (i) the increase of ττ or kk can enhance the stochastic resonance in the signal-to-noise ratio as a function of intrinsic noise strength αα; (ii) on the contrary, the increase of ττ or kk can weaken the stochastic resonance in the signal-to-noise ratio as a function of extrinsic noise strength DD; and (iii) the increase of ττ can lead to double stochastic resonance phenomenon in the signal-to-noise ratio as a function of kk.