Scenario of the Birth of Hidden Attractors in the Chua Circuit

TL;DR

This paper investigates the complex dynamics of the Chua circuit, revealing how hidden and selfexcited chaotic attractors emerge through bifurcations, including pitchfork and Hopf bifurcations, enriching understanding of nonlinear circuit behavior.

Contribution

It introduces a detailed scenario for the emergence of hidden attractors in the Chua circuit, linking bifurcations to attractor birth mechanisms.

Findings

Identification of a pitchfork bifurcation leading to symmetric attractors.

Demonstration of attractor merging and splitting processes.

Discussion of subcritical Hopf bifurcation's role in hidden attractor formation.

Abstract

Recently it was shown that in the dynamical model of Chua circuit both the classical selfexcited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of selfexcited and hidden attractors is studied. It is shown a pitchfork bifurcation in which a pair of symmetric attractors coexists and merges into one symmetric attractor through an attractormerging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near equilibrium points and the birth of hidden attractors is discussed.