This Letter introduces a new method—mode decomposition—for stability analysis of periodic orbits. Using this method, the stability of a periodic solution of an autonomous system, as well as the stability of synchronization within three chaotic systems with linear coupling, can be analyzed. As an example, a rigorous sufficient condition on the coupling coefficients for achieving chaos synchronization is obtained, for the case of three-coupled identical Lorenz systems. Numerical simulations are shown for demonstration.
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