Permanence and extinction of non-autonomous Lotka-Volterra facultative systems with jump-diffusion

Dan  Li; Jing'an  Cui; Yan  Zhang

doi:10.3934/dcdsb.2015.20.2069

Article Contents

2015, Volume 20, Issue 7: 2069-2088. Doi: 10.3934/dcdsb.2015.20.2069

This issue Previous Article Dynamics of stochastic fractional Boussinesq equations Next Article The spreading fronts in a mutualistic model with advection

Permanence and extinction of non-autonomous Lotka-Volterra facultative systems with jump-diffusion

1.
Department of Mathematics, Harbin Institute of Technology, Harbin, 150001
2.
School of Science, Beijing University of Civil Engineering and Architecture, Beijing, 100044

Received: April 30, 2014

Revised: January 31, 2015

Published: August 2015

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Abstract

Using stochastic differential equations with Lévy jumps, this paper studies the effect of environmental stochasticity and random catastrophes on the permanence of Lotka-Volterra facultative systems. Under certain simple assumptions, we establish the sufficient conditions for weak permanence in the mean and extinction of the non-autonomous system, respectively. In particular, a necessary and sufficient condition for permanence and extinction of autonomous system with jump-diffusion are obtained. We generalize some former results under weaker assumptions. Finally, we discuss the biological implications of the main results.

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Mathematics Subject Classification: 60H10, 60J75, 92D25, 62P12.

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