Normal forms and nonlocal chaotic behavior in Sprott systems

Abstract

The Sprott systems are used as benchmarks for investigating the applicability of the normal form transformation in estimating nonlocal properties of attractors such as positive and zero Liapunov exponents. Possibility of a relation between complex conjugate eigenvalue pairs and zero Liapunov exponents; conditions under which the normal form expansion can represent the attractor; an averaging relation for the largest Liapunov exponent based on this representation are studied. Nonlinear transformations that can change the order of a resonance are considered. In spite of their convergence problems, it is seen that the normal form approach can give reasonable estimates of nonlocal properties of attractors near Hopf bifurcations.