Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2013; 50(6): 1847-1854

Printed November 1, 2013

https://doi.org/10.4134/BKMS.2013.50.6.1847

Copyright © The Korean Mathematical Society.

Global asymptotic stability of positive steady states of an $n$-dimensional ratio-dependent predator-prey system with diffusion

Jun Zhou

Southwest University

Abstract

The main concern of this paper is to study the dynamics of an $n$-dimensional ratio-dependent predator-prey system with diffusion. We study the dissipativeness, persistence of the system and it is shown that the unique positive constant steady state is globally asymptotically stable under some assumptions.

Keywords: ratio-dependent response function, global asymptotic stability, iteration method

MSC numbers: 35K57, 92D25