Stability analysis and mapping of multiple dynamics of Chua’s circuit in full four-parameter SpacesV.

Abstract

The stability analysis is used in order to identify and to map different dynamics of Chua’s circuit in full four-parameter spaces. The study is performed using describing functions that allow to identify fixed point, periodic orbit, and unstable states with relative accuracy, as well as to predict route to chaos and hidden dynamics that conventional computational methods do not detect. Numerical investigations based on the computation of eigenvalues and Lyapunov exponents partially support the predictions obtained from the theoretical analysis since they do not capture the multiple dynamics that can coexist in the operation of Chua’s circuit. Attractors obtained from initial conditions outside of neighborhoods of the equilibrium points confirm the multiplicity of dynamics in the operation of Chua’s circuit and corroborate the theoretical analysis.