1998
DOI: 10.1103/physrevlett.80.1642
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Transition to Phase Synchronization of Chaos

Abstract: Phase synchronization of chaos is studied using a modified Rössler system. By employing a lift of the phase variable (i.e., phase points separated by 2p are not considered as the same), the transition to phase synchronization is viewed as a boundary crisis mediated by an unstable-unstable pair bifurcation on a branched manifold, and the accompanying basin boundary structure is found to be of a new type.[S0031-9007(98)05362-9] PACS numbers: 05.45. + b, 02.40.Sf

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Cited by 217 publications
(130 citation statements)
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“…Indeed, close to the threshold parameter values for which the coupled systems show synchronized dynamics, it is observed that the de-synchronization mechanism involves persistent intermittent time intervals during which the synchronized oscillations are interrupted by the non-synchronous behavior. These pre-transitional intermittencies have been described in details for the case of lag synchronization [5,6,7] and for generalized synchronization [8], and their main statistical properties (following those of the on-off intermittency) have been shown to be common to other relevant physical processes.As far as intermittency phenomena near the phase synchronization onset are concerned, two types of intermittent behavior have been observed so far [9,10,11,12], namely the type-I intermittency and the super-long laminar behavior (so called "eyelet intermittency" [13]). …”
mentioning
confidence: 99%
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“…Indeed, close to the threshold parameter values for which the coupled systems show synchronized dynamics, it is observed that the de-synchronization mechanism involves persistent intermittent time intervals during which the synchronized oscillations are interrupted by the non-synchronous behavior. These pre-transitional intermittencies have been described in details for the case of lag synchronization [5,6,7] and for generalized synchronization [8], and their main statistical properties (following those of the on-off intermittency) have been shown to be common to other relevant physical processes.As far as intermittency phenomena near the phase synchronization onset are concerned, two types of intermittent behavior have been observed so far [9,10,11,12], namely the type-I intermittency and the super-long laminar behavior (so called "eyelet intermittency" [13]). …”
mentioning
confidence: 99%
“…As far as intermittency phenomena near the phase synchronization onset are concerned, two types of intermittent behavior have been observed so far [9,10,11,12], namely the type-I intermittency and the super-long laminar behavior (so called "eyelet intermittency" [13]). …”
mentioning
confidence: 99%
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“…In the context of coupled chaotic systems different types of synchronizations have been studied in the past years. These include complete or identical synchronization [15,16,18], phase synchronization [21,24], lag synchronization [25], anticipatory synchronization [26], imperfect phase synchronization [27], generalized synchronization [22,23], measure synchronization in Hamilto- * suman@prl.res.in † amritkar@prl.res.in nian systems [28] etc. Among these the simplest and the most studied is the complete synchronization which occurs in two or more coupled identical dynamical systems and is characterized by the equality of state variables of the interacting systems.…”
Section: Introductionmentioning
confidence: 99%
“…Anishchenko et al 3 have associated this boundary with an accumulation of curves of tangent bifurcations of saddle cycles, and a more recent study by Pikovsky et al 19 suggests that attractor-repeller collisions take place at the transition to chaotic synchronization, thus drawing on the analogy with the tangent bifurcation of a limit cycle. Most recently, 20 the transition to phase synchronization was described as a boundary crisis mediated by unstableunstable pair bifurcations on a branched manifold.…”
Section: Introductionmentioning
confidence: 99%