In this Rapid Communication, a switching manifold approach is proposed for synchronizing chaos. The effectiveness of this nonlinear control strategy is demonstrated by both theoretical analysis and numerical simulations on two typical chaotic systems: the Lorenz and the modified Lorenz systems.

Using the method of variable feedback, synchronization of chaotic and hyperchaotic systems is presented. The robustness of the method based on the flexibility of choices of feedback functions is exemplified. Linear and nonlinear feedback functions and their linear superpositions are used for synchronization. Calculations with model systems indicate that functions constructed by linear superposition of feedback functions that independently synchronize a system are more efficient in achieving synchronization than the functions from which they are made. We have not noticed any difference in the technique of synchronization based on the number of positive Lyapunov exponents. ͓S1063-651X͑97͒09605-0͔

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