Analyzing the Jacobi Stability of Lü’s Circuit System

Abstract

By reformulating the circuit system of Lü as a set of two second order differential equations, we investigate the nonlinear dynamics of Lü’s circuit system from the Jacobi stability point of view, using Kosambi–Cartan–Chern geometric theory. We will determine the five KCC invariants, which express the intrinsic geometric properties of the system, including the deviation curvature tensor. Finally, we will obtain necessary and sufficient conditions on the parameters of the system to have the Jacobi stability near the equilibrium points.

Keywords

• Lü circuit system
• KCC-geometric theory
• the deviation curvature tensor
• Jacobi stability