Based on the invariance principle of differential equations, a simple adaptive-feedback scheme is proposed to strictly synchronize almost all chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically adapted to completely synchronize two almost arbitrary identical chaotic systems, so this scheme is analytical, and simple to implement in practice. Moreover, it is quite robust against the effect of noise. The famous Lorenz and Rössler hyperchaos systems are used as illustrative examples.

• Received 7 June 2004

DOI:https://doi.org/10.1103/PhysRevE.71.037203