Báo Cáo Báo cáo hóa học EXISTENCE AND GLOBAL STABILITY OF POSITIVE PERIODIC SOLUTIONS OF A DISCRETE PREDATOR

EXISTENCE AND GLOBAL STABILITY OF POSITIVE PERIODIC SOLUTIONS OF A DISCRETE PREDATOR-PREY SYSTEM WITH DELAYS LIN-LIN WANG, WAN-TONG LI, AND PEI-HAO ZHAO

Received 13 January 2004


We study the existence and global stability of positive periodic solutions of a periodic discrete predator-prey system with delay and Holling type III functional response. By using the continuation theorem of coincidence degree theory and the method of Lyapunov functional, some sufficient conditions are obtained.


1. Introduction Many realistic problems could be solved on the basis of constructing suitable mathematical models, but it is obvious that a perfect model cannot be achieved because even if we could put all possible factors in a model, the model could never predict ecological catastrophes or mother nature caprice. Therefore, the best we can do is to look for analyzable models that describe as well as possible the reality on populations. From a mathematical point of view, the art of good modelling