Stability Theory of Synchronized Motion in Coupled-Oscillator Systems

The general stability theory of the synchronized motions of the coupled oscillator systems is developed with the use of the extended Lyapunov matrix approach. We give the explicit formula for a stability parameter of the synchronized state W unlf When the coupling strength is weakened, the coupled system may exhibit several types of non synchronized motion. In particular, if W Unlf is chaotic, we always get a transition from chaotic Wunlf to a certain non uniform state and finally the nonuniform chaos. Details associated with such transition are investigated for the coupled Lorenz model. As an application of the theory, we propose a new experimental method to directly measure the positive Lyapunov exponent of intrinsic chaos in reaction systems.