Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system

✍ Scribed by Meng Fan; Ke Wang

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 617 KB
• Volume: 35
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(02)00062-6

✦ Synopsis

With the help of differential equations with piecewise constant arguments, we first propose a discrete analogue of continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modeling the dynamics of the prey and the predator having nonoverlapping generations. Then, easily verifiable sufficient criteria are established for the existence of positive periodic solutions. The approach is based on the coincidence degree and the related continuation theorem as well as some priori estimates. (~) 2002 Elsevier Science Ltd. All rights reserved.

Keywords--Ratio-dependent predator-prey system, Nonautonomous difference equations, Periodic solution, Coincidence degree.

Recently, models with such a prey-dependent-only response function have been facing challenges from biology and physiology communities (see e.g., [11][12][13][14][15][16][17][18]). Based on growing biological and physiological evidences, some biologists have argued that, in many situations, especially