TY - JOUR
T1 - Multivalued mappings in generalized chaos synchronization
AU - Rulkov, Nikolai F.
AU - Afraimovich, Valentin S.
AU - Lewis, Clifford Tureman
AU - Chazottes, Jean Rene
AU - Cordonet, Albert
PY - 2001/1/1
Y1 - 2001/1/1
N2 - 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.
AB - 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.
U2 - 10.1103/PhysRevE.64.016217
DO - 10.1103/PhysRevE.64.016217
M3 - Article
AN - SCOPUS:85035266936
SN - 2470-0045
VL - 64
SP - 11
JO - Physical Review E
JF - Physical Review E
IS - 1
ER -