Four periodic solutions of a generalized delayed predator–prey system. (English) Zbl 1112.34048
This paper is concerned with the existence of multiple positive periodic solutions of a two-predator and one-prey system in which the distributed delay, periodic discrete delay and nonmonotone function response are incorported. By using the continuation theorem of coincidence degree theory, a sufficient condition is given to establish the existence of four positive periodic solutions.
Reviewer: Hai-Feng Huo (Lanzhou)
MSC:
| 34K13 | Periodic solutions to functional-differential equations |
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 92D25 | Population dynamics (general) |
References:
| [1] | Fan, Y. H.; Li, W. T.; Wang, L.-L., Periodic solutions of delay ratio-dependent predator-prey models with monotonic or nonmonotonic functional responses, Nonlinear Analysis:World Application, 5, 247 (2004) · Zbl 1069.34098 |
| [2] | Gaines, R. E.; Mawhin, J. L., Coincidence Degree and Non-linear Differential Equations (1977), Springer: Springer Berlin · Zbl 0339.47031 |
| [3] | Freedman, H. I.; Wu, J., Periodic solutions of single species models with periodic delay, SIAM J. Math. Anal., 23, 689 (1992) · Zbl 0764.92016 |
| [4] | Li, Y.; Kuang, Y., Periodic solutions of periodic delay Lotka-Volterra equations and system, J. Math. Anal. Appl., 255, 260 (2001) · Zbl 1024.34062 |
| [5] | Zhang, Z. Q.; Wang, Z. C., The existence of periodic solution for a generalized prey-predator system with delay, Math. Proc. Canb. Philos. Soc., 137, 475 (2004) · Zbl 1064.34054 |
| [6] | Zhang, Z. Q.; Wang, Z. C., Periodic solution of a two-species ratio-dependent predator-prey system with time delay in a two-patch environment, Anziam J., 45, 233 (2003) · Zbl 1056.34068 |
| [7] | Zhang, Z. Q.; Wang, Z. C., Periodic solution for two-species nonautonomous competition Lotka-Volterra patch-system with time delay, J. Math. Anal. Appl., 365, 35 (2002) |
| [8] | Zhang, Z. Q.; Zeng, X. W., On a periodic stage-structure model, Appl. Math. Lett., 16, 1053 (2003) · Zbl 1050.34061 |
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