In this paper, a practical synchronous criterion of linearly diffusively coupled ordinary differential equations are constructed in with Lyapunov stability theory. The main theorem in this brief paper has extended some corresponding results in the literature. Meanwhile, taking Lorenz Chaotic dynamical network as an example, numerical experiments on some typical linear coupling chaotic dynamical networks, including the regular network, deterministic small-world network, deterministic scale-free network, NW small-world network, BA scale-free network, are carried out to verified the effectiveness of the proposed new theorem.
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