An Exact Solution of Synchronization State for a Class of Networked Mass-Spring-Damper Oscillator Systems

Abstract

This brief paper addresses synchronization dynamics for a class of networked mass-spring-damper oscillator systems. The primary contribution of this work is to give an exact solution of synchronization state for such networked oscillator systems by using tools from matrix theory, algebraic graph theory and the Lyapunov stability theory on dynamical systems. It is explicitly shown that such networked oscillator systems can be synchronized by mild nonlinear network connectivity, even if the isolated oscillator is chaotic or other complex dynamics itself. Furthermore, numerical simulations are given to verify and also visualize the theoretical results