Localization of hidden Chua attractors by the describing function method

TL;DR

This paper applies the describing function method, justified by the small parameter technique, to locate hidden periodic and chaotic attractors in the Chua circuit, introducing a new hidden attractor configuration.

Contribution

It introduces a rigorous approach using the describing function method for localizing hidden attractors in the Chua model, including a novel attractor configuration.

Findings

Successful localization of hidden attractors using the method

Introduction of a new hidden Chua attractor configuration

Validation of the describing function method's effectiveness

Abstract

In this paper the Chua circuit with five linear elements and saturation non-linearity is studied. Numerical localization of self-excited attractor in the Chua circuit model can be done by computation of trajectory with initial data in a vicinity of an unstable equilibrium. For a hidden attractor its basin of attraction does not overlap with a small vicinity of equilibria, so it is difficult to find the corresponding initial data for localization. This survey is devoted to the application of describing function method for localization of hidden periodic and chaotic attractors in the Chua model. We use a rigorous justification of the describing function method, based on the method of small parameter, to get the initial data for the visualization of the hidden attractors. A new configuration of hidden Chua attractors is presented.