Synchronization in stochastic coupled systems: theoretical results
نویسندگان
چکیده
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, Gershgörin 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. PACS numbers: 05.45.Xt, 02.50.Fz, 87.19.La
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