Transforming Analytically Intractable Dynamical Systems with a Control Parameter into a Tractable Ginzburg-Landau Equation: Few Illustrations

Abstract

In the paper a means of making a simplified study of dynamical systems with a control parameter is presented. The intractable, third-order classical Lorenz system, the Lorenz-like Chen system and two topologically dissimilar fifth-order Lorenz systems are considered for illustration. Using the multi-scale method, these systems are reduced to an analytically tractable first-order Ginzburg-Landau equation (GLE) in one of the amplitudes. The analytical solution of the GLE is used to find the remaining amplitudes.