Analytical properties of the Sprott’s chaotic flows

A method is developed to describe the asymptotic (final, at t→∞) behaviour of nonlinear dynamical systems. A systematic examination of all the nineteen chaotic systems proposed by Sprott was preformed by this method. It was found that thirteen of them can be reformulated into oscillatory type second order ordinary differential equations with memory term as forcing one. The rest of the systems cannot be recast in this form, but two of them admit existence of nondifferential relationships between the phase variables at t→∞ The possibility for statistical treatment of the systems in chaotic regime is also discussed. The results could be used for further studies, e.g. numerical analysis of the transient phenomenon.