Limits to the experimental detection of nonlinear synchrony

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 65, Issue 4, 2002, Pages

  So, Paul ^a   Barreto, Ernest ^a   Josić, Krešimir ^b   Sander, Evelyn ^a   Schiff, Steven J ^a  

^a GEORGE MASON UNIVERSITY   (United States)

^b Boston University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; GENERALIZED SYNCHRONIZATION (GS); LYAPUNOV EXPONENT; NONLINEAR SYNCHRONY;

ASYMPTOTIC STABILITY; CONFORMAL MAPPING; GEOMETRY; GRAPH THEORY; LYAPUNOV METHODS; NONLINEAR SYSTEMS; ORDINARY DIFFERENTIAL EQUATIONS; SYNCHRONIZATION; SYSTEM STABILITY;

CHAOS THEORY;

EID: 37649032220     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.65.046225     Document Type: Article

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43. The mechanism for smearing differs fundamentally from this type of multivalueness. The 1:2 multivalued state shown in [24] results from a bifurcation of the response system as the coupling is lowered, while the presence of smearing results from the intrinsic noninvertibility of the drive and is independent of the strength of the coupling. One should note that the examples in Ref. [24] are not globally asymptotically stable. This means that for a given history of the drive, two different initial response states do not necessarily have the same asymptotic state on the m (m = 2 in this case) branches. In contrast, smearing is more "synchronized" in the sense that for a given history of the drive, there is only one unique asymptotic response state despite the unavoidable cantor-like structure of the synchronization set.
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