Dynamics of a class of non-autonomous systems of two non-interacting preys with common predator |
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Authors: | E. M. Elabbasy S. H. Saker |
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Affiliation: | 1. Department of Mathematics, Faculty of Science, Maqnsoura University, 35516, Mansoura, Egypt
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Abstract: | In this paper, we investigate the dynamics of the mathematical model of two non-interacting preys in presence of their common natural enemy (predator) based on the non-autonomous differential equations. We establish sufficient conditions for the permanence, extinction and global stability in the general non-autonomous case. In the periodic case, by means of the continuation theorem in coincidence degree theory, we establish a set of sufficient conditions for the existence of a positive periodic solutions with strictly positive components. Also, we give some sufficient conditions for the global asymptotic stability of the positive periodic solution. |
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