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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. | 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 relies on the following i a sound understanding and appreciation of the biological problem ii a realistic mathematical representation of the important biological phenomena iii finding useful solutions preferably quantitative iv a biological interpretation of the mathematical results in terms of insights and predictions. Usually a mathematical model could be described by two types of systems a continuous system or a discrete one. When the size of the population is rarely small or the population has nonoverlapping generations we may prefer the discrete models. Among all the mathematical models the predator-prey systems play a fundamental and crucial role for more details we refer to 3 6 . In general a predator-prey system may have the form x rx 1 - - pWy 11 y y w x - D where y x is the functional response function. Massive work has been done on this issue. We refer to the monographs 4 10 18 20 for general delayed biological systems and to Copyright 2004 Hindawi Publishing Corporation Advances in .
