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Abstract: In past works, various schemes for adaptive synchronization of chaoticsystems have been proposed. The stability of such schemes is central to theirutilization. As an example addressing this issue, we consider a recentlyproposed adaptive scheme for maintaining the synchronized state of identicalcoupled chaotic systems in the presence of a priori unknown slow temporal driftin the couplings. For this illustrative example, we develop an extension of themaster stability function technique to study synchronization stability withadaptive coupling. Using this formulation, we examine local stability ofsynchronization for typical chaotic orbits and for unstable periodic orbitswithin the synchronized chaotic attractor bubbling. Numerical experimentsillustrating the results are presented. We observe that the stable range ofsynchronism can be sensitively dependent on the adaption parameters, and wediscuss the strong implication of bubbling for practically achievable adaptivesynchronization.



Author: Francesco Sorrentino, Gilad Barlev, Adam B. Cohen, Edward Ott

Source: https://arxiv.org/



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