Reduction Method for Search of Chaotic Attractors in Generic Autonomous Quadratic Dynamical Systems

Abstract

The search method of chaotic attractors for arbitrary [Formula: see text]-dimensional autonomous quadratic dynamical system, which contains at least two nonlinear equations, is presented. This method allows to reduce the search problem to that of chaotic attractors for some two-dimensional nonautonomous quadratic dynamical system with periodic coefficients. Examples of new chaotic attractors in 4D hyperchaotic Rabinovich system and 5D chaotic system arising from double-diffusive convection in a fluid layer, which were found by the Reduction Method, are given.