Stochastic sensitivity analysis of noise-induced excitement in a prey–predator plankton system

Abstract

In this paper, the excitable Truscott–Brindley dynamical model of the interacting populations under environmental noise is considered. We study a probabilistic mechanism of the noise-induced outbreaks in a zone of stable deterministic equilibria. The stochastic sensitivity functions technique and method of confidence ellipses are applied for the description of the spatial arrangement of random states near the deterministic attractor. The effectiveness of our method for the constructive analysis of the stochastic excitement in Truscott–Brindley model is demonstrated. A critical value for the intensity of noise-generating noise-induced outbreaks is estimated.

Keywords:

• noise-induced excitement
• prey–predator system
• stochastic sensitivity function

Acknowledgements

This work was partially supported by Grant RFBR10-01-96022_ural and Federal Target Program Grant No. 1.1099.2011.