Analysis of the noise-induced regimes in Ricker population model with Allee effect via confidence domains technique.

Irina Bashkirtseva,Lev Ryashko

doi:10.1155/2014/346239

Abstract

We consider a discrete-time Ricker population model with the Allee effect under the random disturbances. It is shown that noise can cause various dynamic regimes, such as stable stochastic oscillations around the equilibrium, noise-induced extinction, and a stochastic trigger. For the parametric analysis of these regimes, we develop a method based on the investigation of the dispersions and arrangement of confidence domains. Using this method, we estimate threshold values of the noise generating such regimes.

Highlights

Environmental noise is an inevitable attribute of any living system
A phase trajectory can cross a separatrix between basins of the attraction of coexisting attractors and exhibit new dynamical regimes [5, 8]
Upon reaching a certain critical value of the noise intensity, iterations of the stochastic system (19) with a high probability pass through the unstable equilibrium x1 into the basin of attraction of the stable equilibrium x0 and perform small-amplitude stochastic oscillations near x0

Summary

Introduction

Environmental noise is an inevitable attribute of any living system. Investigations of noise-induced phenomena in biological systems attract the attention of many researchers [1,2,3,4]. We study Allee effect in the discrete-time population Ricker model forced by additive and parametric noises. For the general one-dimensional discrete-time systems with parametric noise, we develop a new analytical method for the approximation of the dispersions of random states around stochastically forced equilibria. We demonstrate constructive abilities of the new approach based on confidence domains technique

Analysis of Stochastic Equilibrium

Analysis of Stochastic Ricker Model with Allee Effect

Conclusion