SYNCHRONIZATION OF CHAOTIC ORBITS - THE INFLUENCE OF UNSTABLE PERIODIC-ORBITS

A chaotic trajectory can be synchronized with a desired unstable orbit (chaotic, periodic, or fixed point) by using a drive variable for whi ch the response subsystem Lyapunov exponents (SLE's) are negative. Une xpectedly, for the Lorenz and Rossler systems, the SLE's obtained for synchronization with the fixed point showed good agreement with those obtained for chaotic orbits. For the Duffing oscillator, a similar agr eement was found between the SLE's of the chaotic orbit and those of t he unstable period-six orbit. It is conjectured that the SLE's of the chaotic orbit retain a memory of the periods of the orbit's origin.