Numerical analysis of noise-induced oscillating bistability in a prey-predator plankton system

Abstract

Stochastic cycles of the Truscott-Brindley (TB) model for predator-prey plankton system are studied. For weak noise, random trajectories are concentrated in the small neighborhood of the unforced deterministic cycle. As the noise intensity increases, in the Canard-like cycles zone of the TB model, the stochastic trajectories begin to split into two parts. This new noise-induced phenomenon is investigated using numerical simulation of random trajectories and stochastic sensitivity functions (SSF) technique. It is shown that the intensity of noise generating this splitting bifurcation significantly depends on the stochastic sensitivity of cycles. Using the SSF technique, we find a critical value of the parameter corresponding to the supersensitive cycle. For this critical value, a comparative parametrical analysis of the stochastic cycle splitting is presented. An interplay of this noise-induced phenomenon with local instability of Canard cycles is discussed.