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Chaos in a periodically forced predator-prey ecosystem model. (English) Zbl 0767.92028
Summary: We subject to periodic forcing the classical Volterra predator-prey ecosystem model, which in its unforced state has a globally stable focus as its equilibrium. The periodic forcing is effected by assuming a periodic variation in the intrinsic growth rate of the prey. In nondimensional form the forced system contains four control parameters, including the forcing amplitude and forcing frequency. Numerical experiments carried out over sections of the parameter space reveal an abundance of steady-state chaotic solutions. We graph Poincaré maps and calculate Lyapunov exponents and fractal dimensions for a representative selection of strange attractors. The transitions to chaos were found to be either via a Feigenbaum cascade of period-doubling bifurcations or via frequency locking.

92D40 Ecology
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
92-08 Computational methods for problems pertaining to biology
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