Elsevier

Applied Mathematics Letters

Volume 25, Issue 11, November 2012, Pages 1980-1985
Applied Mathematics Letters

Stationary distribution, ergodicity and extinction of a stochastic generalized logistic system

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Abstract

This paper is concerned with a stochastic generalized logistic equation dx=x[raxθ]dt+i=1nαixdBi(t)+i=1nβix1+θdBi(t), where Bi(t)(i=1,,n) are independent Brownian motions. We show that if the intensities of the white noises are sufficiently small, then there is a stationary distribution to this equation and it has an ergodic property. If the intensities of the white noises are sufficiently large, then the equation is extinctive. Some numerical simulations are introduced to support the main results at the end.

Keywords

Generalized logistic equation
Stochastic perturbations
Stationary distribution
Ergodic
Extinction

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