Stability analysis of the Chua's circuit with generic odd nonlinearity

Abstract

This paper analyzes the stability of the Chua's circuit with generic odd nonlinearity using two traditional analytical tools of the control theory. The first tool is based on the linear approximation of a nonlinear system for the local stability analysis around equilibrium points or manifolds using the Jacobian matrix eigenvalues, which are mapped in the complex plane using the root locus method. The second tool is an extension of linear techniques based on frequency response known as describing function method, which allows analyze effects of nonlinearities in dynamical systems and predict several nonlinear phenomena with reasonable accuracy. These two analytical tools are jointly applied to the stability analysis of an example of this class of nonlinear systems to identify and map its dynamical behavior in parameter space. Numerical investigations based on computational simulations corroborate the theoretical predictions obtained in this stability analysis.