Permanence and ergodicity of stochastic Gilpin-Ayala population model with regime switching

Hongfu  Yang; Xiaoyue  Li; George Yin

doi:10.3934/dcdsb.2016119

Article Contents

2016, Volume 21, Issue 10: 3743-3766. Doi: 10.3934/dcdsb.2016119

This issue Previous Article Traveling waves in an SEIR epidemic model with the variable total population Next Article Dynamics for the complex Ginzburg-Landau equation on non-cylindrical domains I: The diffeomorphism case

Permanence and ergodicity of stochastic Gilpin-Ayala population model with regime switching

1.
School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024
2.
Center for Mathematics and Interdisciplinary Sciences, School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin 130024
3.
Department of Mathematics, Wayne State University, Detroit, Michigan 48202

Received: October 31, 2015

Revised: May 31, 2016

Published: November 2016

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Abstract

This work is concerned with permanence and ergodicity of stochastic Gilpin-Ayala models involve continuous states as well as discrete events. A distinct feature is that the Gilpin-Ayala parameter and its corresponding perturbation parameter are allowed to be varying randomly in accordance with a random switching process. Necessary and sufficient conditions of the stochastic permanence and extinction are established, which are much weaker than the previous results. The existence of the unique stationary distribution is also established. Our approach treats much wider class of systems, uses much weaker conditions, and substantially generalizes previous results. It is shown that regime switching can suppress the impermanence. Furthermore, several examples and simulations are given to illustrate our main results.

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Mathematics Subject Classification: Primary: 60H10; Secondary: 92B05.

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