Preventing Noise-Induced Extinction in Discrete Population Models

Abstract

A problem of the analysis and prevention of noise-induced extinction in nonlinear population models is considered. For the solution of this problem, we suggest a general approach based on the stochastic sensitivity analysis. To prevent the noise-induced extinction, we construct feedback regulators which provide a low stochastic sensitivity and keep the system close to the safe equilibrium regime. For the demonstration of this approach, we apply our mathematical technique to the conceptual but quite representative Ricker-type models. A variant of the Ricker model with delay is studied along with the classic widely used one-dimensional system.

Stochastic sensitivity analysis of stationary patterns in spatially extended systems

“…The stochastic sensitivity function (SSF) technique was elaborated and successfully applied for the analysis of stochastic phenomena in finite-dimensional systems. [19][20][21][22][23][24][25] Novelty of the present paper is in the analytical approach to estimation of mean-square deviation of random states from the deterministic patterns-attractors. 26 Section 2 introduces the stochastic sensitivity function method for stationary states of spatially distributed systems.…”

Noise‐induced transformations in corporate dynamics of coupled chaotic oscillators

“…[17][18][19] A mathematical analysis of these phenomena is usually carried out in the framework of the theory of stochastic bifurcations. 18,[20][21][22][23][24] Here, the main ones are two types: P-bifurcations associated with a qualitative change in the shape of the distribution of probability density and D-bifurcations associated with a change in the sign of the Lyapunov exponent.…”