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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.
Fujisaka et al. (Sat,) studied this question.