Hidden Bifurcations in the Multispiral Chua Attractor

Abstract

We introduce a novel method revealing hidden bifurcations in the multispiral Chua attractor in the case where the parameter of bifurcation [Formula: see text] which determines the number of spiral is discrete. This method is based on the core idea of the genuine Leonov and Kuznetsov method for searching hidden attractors (i.e. applying homotopy and numerical continuation) but used in a very different way. Such hidden bifurcations are governed by a homotopy parameter [Formula: see text] whereas [Formula: see text] is maintained constant. This additional parameter which is absent from the initial problem is perfectly fitted to unfold the actual structure of the multispiral attractor. We study completely the multispiral Chua attractor, generated via sine function, and check numerically our method for odd and even values of [Formula: see text] from 1 to 12. In addition, we compare the shape of the attractors obtained for the same value of parameter [Formula: see text] while varying the parameter [Formula: see text].