The negative side of Chua’s circuit parameter space : stability analysis, period-adding, basin of attraction metamorphoses, and experimental investigation.

Abstract

Although Chua’s circuit is one of the most studied nonlinear dynamical systems, its version with negative parameters remains practically untouched. This work reports an interesting and rich dynamic scenery that was hidden in this almost unexplored region. The study is focused on 2D parameter space and presents an analysis of stability based on describing functions. Numerical investigations present a gallery of period-adding cascades and a strong presence of basin boundary metamorphoses. The key to this new scenario is that for negative parameters, Chua’s system does not satisfy the Shilnikov condition and it is shown that the homoclinic orbit organizes the parameter space completely different from as known. The obtained experimental results corroborate with the numerical and theoretical investigations.