Analyzing the synchronization of Rössler systems – When trigger-and-reinject is equally important as the spiral motion

The study of the synchronous stability of two coupled Rössler attractors sometimes can be effectively described by approximating the trajectory on the attractor as a planar outward spiral. We show that this is true only when one is dealing with the spiral-type attractor. But when the equally importa...

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Bibliographic Details
Published inPhysics letters. A Vol. 381; no. 42; pp. 3641 - 3651
Main Authors Cheng, An-Liang, Chen, Yih-Yuh
Format Journal Article
LanguageEnglish
Published Elsevier B.V 13.11.2017
Subjects
Funnel-type Rössler attractor
Rössler attractor
Simple core
Synchronization of chaos
Rössler attractor
Funnel-type Rössler attractor
Simple core
Synchronization of chaos
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Summary:The study of the synchronous stability of two coupled Rössler attractors sometimes can be effectively described by approximating the trajectory on the attractor as a planar outward spiral. We show that this is true only when one is dealing with the spiral-type attractor. But when the equally important funnel-type attractor is encountered, a properly constructed time-weighted average must be used to yield a prediction that agrees well with numerical results. We also show analytically how the separation vector evolves in time, and demonstrate why this study matters when one tries to perform the time-weighted average. •Funnel type Rössler attractor can be divided into spiral part and trigger part.•Synchronous stability can be constructed using the time-weighted average of MTLEs.•When ϵ(coupling strength)>ϵ⁎ the separation vector tends to a specific direction.•For trigger part the evolution of separation vector is perturbatively calculated.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2017.09.042