Three Types of Transitions to Phase Synchronization in Coupled Chaotic Oscillators

Grigory V. Osipov; Bambi Hu; Changsong ZHOU; Mikhail V. Ivanchenko; Jrgen Kurths

doi:10.1103/PhysRevLett.91.024101

Three Types of Transitions to Phase Synchronization in Coupled Chaotic Oscillators

Grigory V. Osipov, Bambi Hu, Changsong ZHOU, Mikhail V. Ivanchenko, Jrgen Kurths

Research output: Contribution to journal › Journal article › peer-review

158 Citations (Scopus)

Abstract

We study the effect of noncoherence on the onset of phase synchronization of two coupled chaotic oscillators. Depending on the coherence properties of oscillations characterized by the phase diffusion, three types of transitions to phase synchronization are found. For phase-coherent attractors this transition occurs shortly after one of the zero Lyapunov exponents becomes negative. At rather strong phase diffusion, phase locking manifests a strong degree of generalized synchronization, and occurs only after one positive Lyapunov exponent becomes negative. For intermediate phase diffusion, phase synchronization sets in via an interior crises of the hyperchaotic set.

Original language	English
Journal	Physical Review Letters
Volume	91
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevLett.91.024101
Publication status	Published - 11 Jul 2003

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General Physics and Astronomy

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10.1103/PhysRevLett.91.024101

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@article{153fda4c29e34318a1e92c686eab7dd1,

title = "Three Types of Transitions to Phase Synchronization in Coupled Chaotic Oscillators",

abstract = "We study the effect of noncoherence on the onset of phase synchronization of two coupled chaotic oscillators. Depending on the coherence properties of oscillations characterized by the phase diffusion, three types of transitions to phase synchronization are found. For phase-coherent attractors this transition occurs shortly after one of the zero Lyapunov exponents becomes negative. At rather strong phase diffusion, phase locking manifests a strong degree of generalized synchronization, and occurs only after one positive Lyapunov exponent becomes negative. For intermediate phase diffusion, phase synchronization sets in via an interior crises of the hyperchaotic set.",

author = "Osipov, {Grigory V.} and Bambi Hu and Changsong ZHOU and Ivanchenko, {Mikhail V.} and Jrgen Kurths",

note = "Funding Information: We thank V. Belykh, A. Pikovsky, and M. Rosenblum for useful discussions. This work was supported by the Hong Kong Research Grant Council (RGC) and by the Hong Kong Baptist University Research Grant (FRG) (B. H.), Humboldt Foundation (C. Z.), SFB 555 (J. K.), and INTAS (Project No. 01-2061) (J. K.). G. O. acknowledges support as Visiting Professor in Cognitive Science at the Potsdam University, INTAS (Project No. 01-867) and RFBR (Projects No. 02-02-17573 and No. 03-02-17543). M. I. acknowledges RFBR (Project No. 03-02-06371) and “Dynasty” Foundation.",

year = "2003",

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doi = "10.1103/PhysRevLett.91.024101",

language = "English",

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T1 - Three Types of Transitions to Phase Synchronization in Coupled Chaotic Oscillators

AU - Osipov, Grigory V.

AU - Hu, Bambi

AU - ZHOU, Changsong

AU - Ivanchenko, Mikhail V.

AU - Kurths, Jrgen

N1 - Funding Information: We thank V. Belykh, A. Pikovsky, and M. Rosenblum for useful discussions. This work was supported by the Hong Kong Research Grant Council (RGC) and by the Hong Kong Baptist University Research Grant (FRG) (B. H.), Humboldt Foundation (C. Z.), SFB 555 (J. K.), and INTAS (Project No. 01-2061) (J. K.). G. O. acknowledges support as Visiting Professor in Cognitive Science at the Potsdam University, INTAS (Project No. 01-867) and RFBR (Projects No. 02-02-17573 and No. 03-02-17543). M. I. acknowledges RFBR (Project No. 03-02-06371) and “Dynasty” Foundation.

PY - 2003/7/11

Y1 - 2003/7/11

N2 - We study the effect of noncoherence on the onset of phase synchronization of two coupled chaotic oscillators. Depending on the coherence properties of oscillations characterized by the phase diffusion, three types of transitions to phase synchronization are found. For phase-coherent attractors this transition occurs shortly after one of the zero Lyapunov exponents becomes negative. At rather strong phase diffusion, phase locking manifests a strong degree of generalized synchronization, and occurs only after one positive Lyapunov exponent becomes negative. For intermediate phase diffusion, phase synchronization sets in via an interior crises of the hyperchaotic set.

AB - We study the effect of noncoherence on the onset of phase synchronization of two coupled chaotic oscillators. Depending on the coherence properties of oscillations characterized by the phase diffusion, three types of transitions to phase synchronization are found. For phase-coherent attractors this transition occurs shortly after one of the zero Lyapunov exponents becomes negative. At rather strong phase diffusion, phase locking manifests a strong degree of generalized synchronization, and occurs only after one positive Lyapunov exponent becomes negative. For intermediate phase diffusion, phase synchronization sets in via an interior crises of the hyperchaotic set.

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ER -

Three Types of Transitions to Phase Synchronization in Coupled Chaotic Oscillators

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