Phys. Rev. E 64, 016217 (2001) [11 pages]Multivalued mappings in generalized chaos synchronizationReceived 19 December 2000; published 22 June 2001 The onset of generalized synchronization of chaos in directionally coupled systems corresponds to the formation of a continuous mapping that enables one to persistently define the state of the response system from the trajectory of the drive system. A recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single-valued function. In this paper, we explore generalized synchronization in a regime where the synchronization mapping can become a multivalued function. Specifically, we study the properties of the multivalued mapping that occurs between the drive and response systems when the systems are synchronized with a frequency ratio other than one-to-one, and address the issues of the existence and continuity of such mappings. The basic theoretical framework underlying the considered synchronization regimes is then developed. © 2001 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.64.016217
DOI:
10.1103/PhysRevE.64.016217
PACS:
05.45.Xt, 47.52.+j, 82.40.Bj
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