Assessing the Non-Linear Dynamics of a Hopf–Langford Type System

Abstract

In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of two coupled subsystems in the master (drive)-slave (response) synchronization type. After that, based on the computing first and second Lyapunov values for master system, we have attempted to give a general framework (from bifurcation theory point of view) for understanding the structural stability and bifurcation behavior of original system. Moreover, a family of exact solutions of the master system is obtained and discussed. The effect of synchronization on the dynamic behavior of original system is also studied by numerical simulations.