Stability analysis for the Chua circuit with cubic polynomial nonlinearity based on root locus technique and describing function method

Abstract

This work investigates the dynamics of the Chua circuit with cubic polynomial nonlinearity using methods for stability analysis based on linearization and frequency response. Root locus technique maps eigenvalues of the linearized system in order to analyze the local stability, which allows to verify dynamic features, motion patterns, and attractor topologies. The method based on describing functions allows analyze effects of the cubic nonlinearity in the system, as well as predict equilibrium and fixed points, periodic and chaotic orbits, limit cycles, multistability and hidden dynamics, unstable states, and bifurcations. The stability of the Chua circuit with cubic polynomial nonlinearity is analyzed using both approaches in order to identify and map dynamics in parameter spaces. Numerical investigations based on computational simulations corroborate the theoretical results obtained using this stability analysis. This theoretical analysis and the numerical investigations present interesting insights about the dynamics of the Chua circuit with cubic polynomial nonlinearity and provides a design tool for electro-electronic implementations.