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Zbl 1221.34187
Gakkhar, Sunita; Negi, Kuldeep; Sahani, Saroj Kumar
Effects of seasonal growth on ratio dependent delayed prey predator system. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 14, No. 3, 850-862 (2009). ISSN 1007-5704

Summary: The Beddington--DeAngelis ratio dependent prey predator model with time delay is discussed. The existence of Hopf bifurcation is established. The numerical simulations have shown that seasonal growth and delay can give rise to variety of attractors including periodic, quasi-periodic as well as chaotic oscillations. The degree of complexity in the system increases with increasing magnitude of delay, or frequency of seasonal variation. The model parameters involved in functional response can also affect the complexity of the system.

MSC 2000:: *34K18 Bifurcation theory of functional differential equations
92D25 Population dynamics

Keywords: bifurcation; chaos; delay; seasonality; stability

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Zentralblatt MATH Berlin [Germany]