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Chaos in seasonally perturbed ratio-dependent prey–predator system. (English) Zbl 1033.92026
Summary: We investigate the effects of periodic forcing, in the intrinsic growth rate of the prey, on the Holling–Tanner ratio-dependent prey–predator system. Lyapunov exponents, Lyapunov dimension, and Poincare section are obtained for section of the parametric space for the resulting forced system. The abundance of steady state chaotic solutions is detected when seasonality is superimposed on the system, which otherwise has a globally stable equilibrium state or globally stable limit cycle. The results support the conjecture that seasons can very easily give rise to complex population dynamics.

MSC:
92D25 Population dynamics (general)
92D40 Ecology
37N25 Dynamical systems in biology
34C60 Qualitative investigation and simulation of ordinary differential equation models
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Software:
Dynamics
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