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Chaos in low-dimensional Lotka-Volterra models of competition. (English) Zbl 1107.92058

Summary: The occurrence of chaos in basic Lotka-Volterra models of four competing species is studied. A brute-force numerical search conditioned on the largest Lyapunov exponent (LE) indicates that chaos occurs in a narrow region of the parameter space but is robust to perturbations. The dynamics of the attractor for a maximally chaotic case are studied using symbolic dynamics, and the question of self-organized critical behaviour (scale-invariance) of the solution is considered.

MSC:

92D40 Ecology
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37B10 Symbolic dynamics
37N25 Dynamical systems in biology
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