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Order and chaos in predator to prey ratio-dependent food chain. (English) Zbl 1068.92044

Summary: We investigate the dynamical behavior and chaos of a realistic three species food chain model considering predator to prey ratio-dependence for the interaction together with type II functional response. The model, for biologically reasonable parameter values, exhibits stable, periodic and chaotic dynamics in long-time behavior. Bifurcation diagrams have been obtained, and Lyapunov exponents and dimensions have been computed. The model shows rich dynamics in the positive octant. The dynamical behavior is found to be very sensitive to parameter values and initial data.

MSC:

92D40 Ecology
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
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