Abstract
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.
Highlights
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
A mathematical model could be described by two types of systems: a continuous system or a discrete one
Systems with Holling-type functional response have been investigated by many authors, see, for example, Hsu and Huang [13], Rosenzweig and MacArthur [22, 23]
Summary
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. 322 Existence and stability of periodic solutions [2, 8, 9, 11, 21, 24] for investigation on predator-prey systems. Systems with Holling-type functional response have been investigated by many authors, see, for example, Hsu and Huang [13], Rosenzweig and MacArthur [22, 23]. They studied the stability of the equilibria, existence of Hopf bifurcation, limit cycles, homoclinic loops, and even catastrophe. Motivated by the above considerations, we will consider the discrete predator-prey system with Holling type III functional response. In the rest of this paper, for biological reasons, we only consider solutions N(k) with
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