46,935 research outputs found
The stability of adaptive synchronization of chaotic systems
In past works, various schemes for adaptive synchronization of chaotic
systems have been proposed. The stability of such schemes is central to their
utilization. As an example addressing this issue, we consider a recently
proposed adaptive scheme for maintaining the synchronized state of identical
coupled chaotic systems in the presence of a priori unknown slow temporal drift
in the couplings. For this illustrative example, we develop an extension of the
master stability function technique to study synchronization stability with
adaptive coupling. Using this formulation, we examine local stability of
synchronization for typical chaotic orbits and for unstable periodic orbits
within the synchronized chaotic attractor (bubbling). Numerical experiments
illustrating the results are presented. We observe that the stable range of
synchronism can be sensitively dependent on the adaption parameters, and we
discuss the strong implication of bubbling for practically achievable adaptive
synchronization.Comment: 21 pages, 6 figure
Slower Speed and Stronger Coupling: Adaptive Mechanisms of Self-Organized Chaos Synchronization
We show that two initially weakly coupled chaotic systems can achieve
self-organized synchronization by adaptively reducing their speed and/or
enhancing the coupling strength. Explicit adaptive algorithms for
speed-reduction and coupling-enhancement are provided. We apply these
algorithms to the self-organized synchronization of two coupled Lorenz systems.
It is found that after a long-time self-organized process, the two coupled
chaotic systems can achieve synchronization with almost minimum required
coupling-speed ratio.Comment: 4 pages, 5 figure
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