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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 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.

This report investigates the dynamical stability conjectures of Palis and Smale and Pugh and Shub from the standpoint of numerical observation and lays the foundation for a stability conjecture. As the dimension of a dissipative dynamical system is increased, it is observed that the number of positive Lyapunov exponents increases monotonically, the Lyapunov exponents tend towards continuous change with respect to parameter variation, the number of observable periodic windows decreases (at least below numerical precision) and a subset of parameter space exists such that topological change is very common with small parameter perturbation. However, this seemingly inevitable topological variation is never catastrophic (the dynamic type is preserved) if the dimension of the system is high enough.

The problem of keeping an attention level is one of the common symptoms of attention deficit disorder. Dopamine deficiency is introduced as one of the causes of this disorder. Based on some physiological facts about the attention control mechanism and chaos intermittency, a behavioral model is presented in this paper. This model represents the problem of undesired alternation of attention level, and can also suggest different valuable predictions about a possible cause of attention deficit disorder. The proposed model reveals that there is a possible interaction between different neurotransmitters which help the individual to adaptively inhibit the attention switching over time. The result of this study can be used to examine and develop a new practical and more appropriate treatment for the problem of sustaining attention. [ABSTRACT FROM AUTHOR]