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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:
 34C60 Qualitative investigation and simulation of models (ODE) 92D25 Population dynamics (general) 34C25 Periodic solutions of ODE 47N20 Applications of operator theory to differential and integral equations
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##### References:
 [1] Ma, Z.: Mathematical modelling and studing on species ecology. (1996) [2] Thieme, Horst R.: Mathematics in population biology. Princeton syries in theoretial and computational biology (2003) · Zbl 1054.92042 [3] Gaines, R.; Mawhin, J.: Coincidence degree and nonlinear differetial equitions. (1977) · Zbl 0339.47031 [4] Chen, Y.: Multiple periodic solutions of delayed predator--prey systems with type IV functional responses. Nonlinear anal. Real world appl. 5, 45-53 (2004) · Zbl 1066.92050 [5] Wang, Q.; Dai, B.; Chen, Y.: Multiple periodic solutions of an impulsive predator--prey model with Holling-type IV functional response. Math. comput. Modelling 49, 1829-1836 (2009) · Zbl 1171.34341 [6] D. Hu, Z. Zhang, Four positive periodic solutions to a Lotka--Volterra cooperative system with harvesting terms, Nonlinear Anal. Real World Appl., in press (doi:10.1016/j.nonrwa.2009.02.002) · Zbl 1187.34050