Synchronization in stochastic coupled systems: theoretical results

The stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in stochastic coupled dynamical systems (ordinary differential equations) is considered. A general approach is presented, based on the master stability function, Gershg¨ orin disc theory and the extreme value theory in statistics, to yield constraints on the distribution of coupling to ensure the stability of synchronized dynamics. Three types of different behaviour: global-stable, exponential-stable and power-stable, are found, depending on the nature of the distribution of the interactions between units. Systems with specific coupling schemes are used as examples to illustrate our general method.

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