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Periodic solutions for a semi-ratio-dependent predator–prey system with functional responses. (English) Zbl 1079.34515

The author considers a class of nonautonomous semi-ratio-dependent predator-prey systems with functional response. By using the coincidence degree theory, he obtains sufficient conditions for the existence of a positive periodic solution.

MSC:

34C25 Periodic solutions to ordinary differential equations
92D25 Population dynamics (general)
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References:

[1] Wang, Q.; Fan, M.; Wang, K., Dynamics of a class of nonautonomous semi-ratio-dependent predator-prey system with functional responses, J. Math. Anal. Appl., 278, 443-471 (2003) · Zbl 1029.34042
[2] Leslie, P. H., Some further notes on the use of matrices in population mathematics, Biometrika, 35, 213-245 (1948) · Zbl 0034.23303
[3] Leslie, P. H., A stochastic model for studying the properties of certain biological systems by numerical methods, Biometrika, 45, 16-31 (1958) · Zbl 0089.15803
[4] Pielou, E. C., Mathematical Ecology (1977), John & Sons: John & Sons New York · Zbl 0259.92001
[5] Huo, H. F.; Li, W. T., Periodic solutions of delayed Leslie-Gower predator-prey models, Appl. Math. Comput., 155, 591-605 (2004) · Zbl 1060.34039
[6] Gaines, R. E.; Mawhin, J. L., Coincidence Degree and Nonlinear Differential Equations (1977), Springer: Springer Berlin · Zbl 0326.34021
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