Periodic solutions and homoclinic bifurcation of a predator–prey system with two types of harvesting
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In this paper, a predator–prey model with both constant rate harvesting and state dependent impulsive harvesting is analyzed. By using differential equation geometry theory and the method of successor functions, the existence, uniqueness and stability of the order one periodic solution have been studied. Sufficient conditions which guarantee the nonexistence of order k (k≥2) periodic solution are given. We also present that the system exhibits the phenomenon of homoclinic bifurcation under some parametric conditions. Finally, some numerical simulations and biological explanations are given.
KeywordsPredator–prey system Order k periodic solution Successor function Orbitally asymptotically stable Homoclinic bifurcation
This work is supported by the National Natural Science Foundation of China (11171284), the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (104200510011), program for Innovative Research Team (in Science and Technology) in University of Henan Province (2010IRTSTHN006) and Sci-tech program project of Henan Province (122300410034).
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