A simple adaptive-feedback controller for high-quality chaos synchronization

Based on the invariance principle of differential equations, a simple uniform coupling scheme is proposed to strictly synchronize almost all chaotic systems. Namely, one may synchronize highqualitatively chaotic systems by the uniform adaptive-feedback controller, i.e., a simple feedback coupling with the updated feedback strength. Unlike the usual linear feedback, the variable feedback strength is automatically adapted to synchronize two almost arbitrary identical chaotic systems, and such technique does not require to determine numerically any additive parameters. So this scheme is analytical, and simple to implement in practice. Moreover it is quite robust against the effect of noise. The well-known models such as Lorenz and Rössler hyperchaos systems are used to illustrate the validity of this theoretic method.