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Multiple positive periodic solutions for a generalized predator-prey system with exploited terms. (English) Zbl 1145.34051

The authors consider a delayed periodic generalized predator-prey system with multiple exploited terms. The system models the dynamics of two predators for a prey and the delay is due to gestation. Sufficient conditions are given to guarantee that the system admits at least eight positive periodic solutions. The main result is established by employing the continuation theorem of coincidence degree theory.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K13 Periodic solutions to functional-differential equations
92D25 Population dynamics (general)
47N20 Applications of operator theory to differential and integral equations
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References:

[1] Gaines, R. E.; Mawhin, J. L., Coincidence Degree and Nonlinear Differential Equations (1977), Springer: Springer Berlin · Zbl 0339.47031
[2] Ma, Z. E., Mathematical Modeling and Studying on Species Ecology (1996), Education Press: Education Press Hefei, (in Chinese)
[4] Tian, D. S.; Zeng, X. W., Existence of at least two periodic solutions of a ratio-dependent predator-prey model with exploited term, Acta Math. Appl. Sin. English Series, 21, 3, 489-494 (2005) · Zbl 1098.92072
[5] Zhang, Z. Q.; Wang, H. L., Existence and global attractivity of a positive periodic solution for a generalized prey-predator system with time delay, Math. Comput. Modeling, 44, 188-203 (2006) · Zbl 1160.34066
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