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Periodic solutions of a stage-structured plant-hare model with toxin-determined functional responses. (English) Zbl 1469.34093

Summary: The purpose of this paper is to obtain some sufficient conditions for the global existence of multiple positive periodic solutions of a delayed stage-structured plant-hare model with a toxin-determined functional response. Some novel estimation techniques to construct two open subsets for a priori bounds are employed.

MSC:

34K13 Periodic solutions to functional-differential equations
92D25 Population dynamics (general)
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[1] Song, Y. L.; Peng, Y.; Wei, J. J., Bifurcations for a predator-prey system with two delays, Journal of Mathematical Analysis and Applications, 337, 1, 466-479 (2008) · Zbl 1132.34053 · doi:10.1016/j.jmaa.2007.04.001
[2] Yuan, S. L.; Song, Y. L., Stability and Hopf bifurcations in a delayed Leslie-Gower predator-prey system, Journal of Mathematical Analysis and Applications, 355, 1, 82-100 (2009) · Zbl 1170.34051 · doi:10.1016/j.jmaa.2009.01.052
[3] Song, Y. L.; Yuan, S. L., Bifurcation analysis for a regulated logistic growth model, Applied Mathematical Modelling, 31, 9, 1729-1738 (2007) · Zbl 1167.34377 · doi:10.1016/j.apm.2006.06.006
[4] Xia, Y. H.; Han, M., New conditions on the existence and stability of periodic solution in Lotka-Volterra’s population system, SIAM Journal on Applied Mathematics, 69, 6, 1580-1597 (2009) · Zbl 1181.92084 · doi:10.1137/070702485
[5] Zhang, T.; Liu, J.; Teng, Z., Existence of positive periodic solutions of an SEIR model with periodic coefficients, Applications of Mathematics, 57, 6, 601-616 (2012) · Zbl 1274.34150 · doi:10.1007/s10492-012-0036-5
[6] Xia, Y. H., Global asymptotic stability of an almost periodic nonlinear ecological model, Communications in Nonlinear Science and Numerical Simulation, 16, 11, 4451-4478 (2011) · Zbl 1219.92069 · doi:10.1016/j.cnsns.2011.03.041
[7] Xia, Y. H., Global analysis of an impulsive delayed Lotka-Volterra competition system, Communications in Nonlinear Science and Numerical Simulation, 16, 3, 1597-1616 (2011) · Zbl 1221.34206 · doi:10.1016/j.cnsns.2010.07.014
[8] Xia, Y.; Yuan, X.; Kou, K. I.; Wong, P. J. Y., Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy, Abstract and Applied Analysis, 2014 · Zbl 1468.34083
[9] Xia, Y. H., Periodic solution of certain nonlinear differential equations: via topological degree theory and matrix spectral theory, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 22, 8 (2012) · Zbl 1258.34114 · doi:10.1142/S0218127412501969
[10] Yin, L.; Zhang, Z., Existence of a positive solution for a first-order p-Laplacian BVP with impulsive on time scales, Journal of Applied Analysis and Computation, 2, 1, 103-109 (2012) · Zbl 1304.34048
[11] Gu, X.; Wang, H.; Wong, P.; Xia, Y. H., Existence and stability of periodic solution to delayed nonlinear differential equations, Abstract and Applied Analysis, 2014 (2014) · Zbl 1470.34178 · doi:10.1155/2014/156948
[12] Ding, W.; Han, M., Dynamic of a non-autonomous predator-prey system with infinite delay and diffusion, Computers & Mathematics with Applications, 56, 5, 1335-1350 (2008) · Zbl 1155.34329 · doi:10.1016/j.camwa.2008.03.001
[13] Gao, Y. F.; Wong, P. J. Y.; Xia, Y. H.; Yuan, X., Multiple periodic solutions of a nonautonomous plant-hare model, Abstract and Applied Analysis, 2014 (2014) · Zbl 1470.34117 · doi:10.1155/2014/130856
[14] Aiello, W. G.; Freedman, H. I., A time-delay model of single-species growth with stage structure, Mathematical Biosciences, 101, 2, 139-153 (1990) · Zbl 0719.92017 · doi:10.1016/0025-5564(90)90019-U
[15] Wang, W.; Chen, L., A predator-prey system with stage-structure for predator, Computers & Mathematics with Applications, 33, 8, 83-91 (1997) · doi:10.1016/S0898-1221(97)00056-4
[16] Xia, Y. H.; Cao, J.; 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 · doi:10.1016/j.apm.2006.08.012
[17] Gaines, R. E.; Mawhin, J. L., Coincidence Degree, and Nonlinear Differential Equations. Coincidence Degree, and Nonlinear Differential Equations, Lecture Notes in Mathematics (1977), Berlin, Germany: Springer, Berlin, Germany · Zbl 0339.47031
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