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Interesting synchronization-like behavior. (English) Zbl 1084.37506

Summary: We analyze the behavior of some coupled chaotic systems, which are synchronization-like. This phenomenon occurs when all conditional Lyapunov exponents of a system are not negative. Recently, J. W. Shuaiet, K. W. Wong and L. M. Cheng [Synchronization of spatiotemporal chaos positive conditional Lyapunov exponents, Phys. Rev. E56, 2272–2275 (1997)] observed that synchronization can be achieved even with positive conditional Lyapunov exponents. Here, we review this observation, and, based on this observation, we see that not only interesting synchronization behaviors occur with positive or zero conditional Lyapunov exponents, but also these behaviors depend on different eigenvalues of the linearized system describing the evolution of the difference between the pair of chaotic systems.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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