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Synchronization in networked mass-spring-damper oscillator systems

This brief paper considers synchronization dynamics in networked mass-spring-damper (MSD) oscillator systems with nonlinear spring interaction. Based on stability theory on dynamical system, algebraic graph theory, and some matrix theory, an exact solution of synchronization state for such networked oscillator systems is derived analytically. It is shown that the networked MSD oscillator systems can be synchronized to a simple harmonic motion, even if the isolated oscillator is chaotic or others complex dynamics. Finally, the results are applied to a typical chain networked mechanical systems composing of six MSD oscillators and numerical simulations are given to verify the correctness of the theoretical results.