Báo Cáo Báo cáo hóa học PERIODIC SOLUTIONS OF A DISCRETE-TIME DIFFUSIVE SYSTEM GOVERNED BY BACKWARD DIFFEREN

PERIODIC SOLUTIONS OF A DISCRETE-TIME DIFFUSIVE SYSTEM GOVERNED BY BACKWARD DIFFERENCE EQUATIONS BINXIANG DAI AND JIEZHONG ZOU Received 22 November 2004 and in revised form 16 January 2005 A discrete-time delayed diffusion model governed by backward difference equations is investigated. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable sufficient criteria are established for the existence of positive periodic solutions.

1. Introduction

Recently, some biologists have argued that the ratio-dependent predator-prey model is more appropriate than the Gauss-type models for modelling predator-prey interactions where predation involves searching processes. This is strongly supported by numerous laboratory experiments and observations [1, 2, 3, 4, 10, 11, 12]. Many authors [1, 5, 7, 13, 14] have observed that the ratio-dependent predator-prey systems exhibit much richer, more complicated, and more reasonable or