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Four positive periodic solutions of a discrete time delayed predator-prey system with nonmonotonic functional response and harvesting. (English) Zbl 1165.34400

Summary: By employing the continuation theorem of coincidence degree theory, we establish an easily verifiable criteria for the existence of at least four positive periodic solutions for a discrete time delayed predator-prey system with nonmonotonic functional response and harvesting.

MSC:

34K13 Periodic solutions to functional-differential equations
92D25 Population dynamics (general)
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References:

[1] Berryman, A. A., The origins and evolution of predator-prey theory, Ecology, 75, 1530-1535 (1992)
[2] Fan, Y. H.; Li, W. T.; Wang, L. L., Periodic solutions of delayed ratio-dependent predator-prey models with monotonic or nonmonotonic functional responses, Nonlinear Analysis: RWA, 5, 247-263 (2004) · Zbl 1069.34098
[3] Fan, M.; Wang, K., Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system, Mathematical and Computer Modelling, 35, 951-961 (2002) · Zbl 1050.39022
[4] Li, Y., Periodic solutions of a periodic delay predator-prey system, Proceedings of the American Mathematical Society, 127, 1331-1335 (1999) · Zbl 0917.34057
[5] Zhang, Z. Q.; Wang, Z. C., The existence of a periodic solution for a generalized predator-prey system with delay, Mathematical Proceedings of the Cambridge Philosophical Society, 137, 475-486 (2004) · Zbl 1064.34054
[6] Chen, Y., Multiple periodic solutions of delayed predator-prey system with type IV functional responses, Nonlinear Analysis: RWA, 5, 45-53 (2004) · Zbl 1066.92050
[7] Zhang, Z. Q., Multiple periodic solutions of a generalized predator-prey system with delays, Mathematical Proceedings of the Cambridge Philosophical Society, 141, 175-188 (2006) · Zbl 1105.34045
[8] Xia, Y. H.; Cao, J. D., Global attractivity of a periodic ecological model with \(m\)-predators and \(n\)-preys by pure-delay type system, Computers and Mathematics with Applications, 52, 6-7, 829-852 (2006) · Zbl 1135.34038
[9] Xia, Y. H.; Cao, J. D.; Cheng, S. S., Multiple periodic solutions of a delayed stage-structured predator-prey model with non-monotone functional responses, Applied Mathematical Modelling, 31, 9, 1947-1959 (2007) · Zbl 1167.34342
[10] Xia, Y. H.; Cao, J. D., Almost periodicity in an ecological model with \(M\)-predators and \(N\)-preys by pure-delay type system, Nonlinear Dynamics, 39, 3, 275-304 (2005) · Zbl 1093.92061
[11] Xia, Y. H.; Cao, J. D.; Lin, M. R., Discrete-time analogues of predator-prey models with monotonic or nonmonotonic functional responses, Nonlinear Analysis: RWA, 8, 4, 1079-1095 (2007) · Zbl 1127.39038
[12] Zhang, N., Periodic solutions of a discrete time stage-structure model, Nonlinear Analysis: RWA, 8, 27-39 (2007) · Zbl 1113.39015
[13] Gaines, R. E.; Mawhin, J. L., Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag: Springer-Verlag Berlin · Zbl 0326.34021
[14] Zhang, R. Y., Periodic solutions of a single species discrete population model with periodic harvest/stock, Computers and Mathematics with Applications, 39, 77-90 (2000) · Zbl 0970.92019
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