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Multiple positive periodic solutions for a non-autonomous stage-structured predatory-prey system with harvesting terms. (English) Zbl 1222.37100

Summary: We are concerned with a non-autonomous stage-structured predator-prey model with harvesting terms. By means of the coincidence degree theory, we establish the existence of at least eight positive periodic solutions for the system under consideration. An example is given to illustrate the effectiveness of our results.

MSC:

37N25 Dynamical systems in biology
92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations
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[1] Ma, Z., Mathematical modelling and studing on species ecology (1996), Education Press: Education Press Hefei, [in Chinese]
[2] Thieme, H. R., Mathematics in population biology, (Princeton syries in theoretial and computational biology (2003), Princeton University Press: Princeton University Press Princeton, NJ) · Zbl 1054.92042
[3] Fang, H.; Xiao, Y., Existence of multiple periodic solutions for delay Lotka-Volterra competition patch systems with harvesting, Appl Math Model, 33, 1086-1096 (2009) · Zbl 1168.34349
[4] Berezansky, L.; Braverman, E.; Idels, L., Delay differential logistic equation with harvesting, Math Comput Model, 40, 1509-1525 (2004)
[5] Negi, K.; Gakkhar, S., Dynamics in a Beddington-DeAngelis prey-predator system with impulsive harvesting, Ecol Model, 206, 421-430 (2007)
[6] Z. Zhang, Z. Hou, Existence of four positive periodic solutions for a ratio-dependent predator-prey system with multiple exploited (or harvesting) terms. Nonlinear Anal. Real World Appl., in press. doi:10.1016/j.nonrwa.2009.03.00.; Z. Zhang, Z. Hou, Existence of four positive periodic solutions for a ratio-dependent predator-prey system with multiple exploited (or harvesting) terms. Nonlinear Anal. Real World Appl., in press. doi:10.1016/j.nonrwa.2009.03.00.
[7] Gaines, R.; Mawhin, J., Coincidence degree and nonlinear differetial equitions (1977), Springer Verlag: Springer Verlag Berlin
[8] 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
[9] Wang, Q.; Dai, B.; Chen, Y., Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response, Math Comput Model, 49, 1829-1836 (2009) · Zbl 1171.34341
[10] Hu D, Zhang Z. 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.; Hu D, Zhang Z. 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.
[11] Feng, J.; Chen, S., Four periodic solutions of a generalized delayed predator-prey system, Appl Math Comput, 181, 932-939 (2006) · Zbl 1112.34048
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