Jacobi Stability of the Muthuswamy-Chua-Ginoux Circuit System

The three-dimensional Muthuswamy-Chua-Ginoux (MCG) circuit system based on a thermistor is a generalization of the classical Muthuswamy-Chua circuit differential model. In this paper, the Jacobi stability of the MCG circuit system is analyzed by using the Kosambi-Cartan-Chern (KCC) theory. First, we reformulate the MCG system as a set of two second-order nonlinear differential equations. The geometric invariants associated to this system (nonlinear and Berwald connections), and the deviation curvature tensor, as well as its eigenvalues, are explicitly obtained. The Jacobi stability of the MCG system at an equilibrium point and two periodic orbits is investigated in terms of the eigenvalues of the deviation curvature tensor. The obtained results show that the origin is Jacobi unstable, and the two periodic orbits of the MCG system are also proved to be Jacobi unstable. Finally, we discuss the dynamical behavior of the components of the deviation vector near the equilibrium point.