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In this paper, we investigate the persistence of a class environment mathematical model with delays, the existence and the global stability of its global positive periodic solution by using Comparability Theorem, Coincidence Degree Theory and Lyapunov functions. We obtain the sufficient conditions which guarantee the existence of the global asymptotic stable positive periodic solution of the periodic...
In this paper, we investigate a n-patches nonautonomous predator-prey system with nonlinear diffusion. By the comparison theorem, the sufficient conditions are derived for uniform persistence of the system. We also prove the existence of positive periodic solution of the system by using Schauder's fixed point theorem. Furthermore, the sufficient conditions for global asymptotical stability of positive...
This paper presents a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous Volterra integro-differential equations. Existence is established using a fixed point theorem in cones. We illustrate our theory be examining several biomathematical models.
Some species are cannibalistic and their lives can be divided into several stages. When this kind of species is predator, a stage-structured species model with time delay, Holling type IV functional response and cannibalism can be formulated. The sufficient condition for existence of positive periodic solution is obtained by using coincidence degree theory. Some new results are obtained.
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