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Four positive periodic solutions to a periodic Lotka-Volterra predatory-prey system with harvesting terms. (English) Zbl 1201.34074
A two-species predator-prey system of Lotka-Volterra type that includes harvesting terms, can have four equilibria in the positive quadrant. In this paper, it is assumed that all the parameters of such a system are positive p-periodic continuous functions. The authors make use of Mawhin’s continuation theorem of coincidence degree theory to prove that, under certain inequality assumptions on the periodic parameters, there exist (at least) four p-periodic solutions of the given system. Finally, a numerical example of such a system is presented that satisfies all the assumptions of the theorem.

MSC:
34C60Qualitative investigation and simulation of models (ODE)
92D25Population dynamics (general)
34C25Periodic solutions of ODE
47N20Applications of operator theory to differential and integral equations