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 indicates that chaos occurs in a narrow region of parameter space but is robust to perturbations. The dynamics of the attractor are studied using symbolic dynamics, and the question of self-organized critical behavior (scale-invariance) of the solution is considered.

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Recently, a great advance has been made in the study of sweeping process variational inequalities with the papers (Chemetov, Monteiro Marques Set-Valued Anal. 15, 209-221, 2007; where, for a prox-regular moving set depending on both the time and the state, several existence results are provided. Those authors also studied the case where such a differential inclusion is perturbed by multimapping. The present paper establishes the existence of solutions for such perturbed differential inclusions in some context not considered in the previous papers.