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Modulation of nonlinear coupling on the synchronization induced by linear coupling. (Chinese. English summary) Zbl 1289.37017
Summary: Based on the Lyapunov stability theory, a Lyapunov function of exponential type is constructed. The four-variable Chen hyperchaotic model is investigated as an example. The reliability of a linear coupling-induced synchronization of a hyperchaotic system is proved analytically. Furthermore, the modulation effect of the nonlinear coupling on the synchronization induced by the linear coupling is investigated. A statistical function is defined to evaluate the power consumption of the controller according to the dimensionless dynamical equations, and the appropriate parameter region for the synchronization due to the joint action of the linear and nonlinear coupling. The extensive numerical results confirm the correctness of the theoretical predictions.

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34D06 Synchronization of solutions to ordinary differential equations