Noise Induced Jumping Dynamics between Synchronized Modes

Shannon Algar; Thomas Stemler; B. De Saedeleer

doi:10.1142/S0218127415300347

Noise Induced Jumping Dynamics between Synchronized Modes

Shannon Algar, Thomas Stemler, B. De Saedeleer

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

© 2015 World Scientific Publishing Company. Synchronization is a common phenomenon whereby a dynamical system follows the pacemaker provided by an external forcing. Often, such systems have multiple synchronization modes, which are equivalent solutions. We investigate the specific case of two to one synchronization produced by the periodic forcing of a van der Pol oscillator where two possible modes, shifted by one period of the modulation, exist. By studying the flow and the local Lyapunov exponents along the orbit we give an explanation of the noise induced jumps observed in a stochastic forced oscillator. While this investigation gives results that are specific to this system, the framework presented is more general and can be applied to any system showing similar jumping dynamics.

Original language	English
Pages (from-to)	1530034
Journal	International Journal of Bifurcation and Chaos
Volume	25
Issue number	12
DOIs	https://doi.org/10.1142/S0218127415300347
Publication status	Published - 2015

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abstract = "{\textcopyright} 2015 World Scientific Publishing Company. Synchronization is a common phenomenon whereby a dynamical system follows the pacemaker provided by an external forcing. Often, such systems have multiple synchronization modes, which are equivalent solutions. We investigate the specific case of two to one synchronization produced by the periodic forcing of a van der Pol oscillator where two possible modes, shifted by one period of the modulation, exist. By studying the flow and the local Lyapunov exponents along the orbit we give an explanation of the noise induced jumps observed in a stochastic forced oscillator. While this investigation gives results that are specific to this system, the framework presented is more general and can be applied to any system showing similar jumping dynamics.",

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AU - Stemler, Thomas

AU - De Saedeleer, B.

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N2 - © 2015 World Scientific Publishing Company. Synchronization is a common phenomenon whereby a dynamical system follows the pacemaker provided by an external forcing. Often, such systems have multiple synchronization modes, which are equivalent solutions. We investigate the specific case of two to one synchronization produced by the periodic forcing of a van der Pol oscillator where two possible modes, shifted by one period of the modulation, exist. By studying the flow and the local Lyapunov exponents along the orbit we give an explanation of the noise induced jumps observed in a stochastic forced oscillator. While this investigation gives results that are specific to this system, the framework presented is more general and can be applied to any system showing similar jumping dynamics.

AB - © 2015 World Scientific Publishing Company. Synchronization is a common phenomenon whereby a dynamical system follows the pacemaker provided by an external forcing. Often, such systems have multiple synchronization modes, which are equivalent solutions. We investigate the specific case of two to one synchronization produced by the periodic forcing of a van der Pol oscillator where two possible modes, shifted by one period of the modulation, exist. By studying the flow and the local Lyapunov exponents along the orbit we give an explanation of the noise induced jumps observed in a stochastic forced oscillator. While this investigation gives results that are specific to this system, the framework presented is more general and can be applied to any system showing similar jumping dynamics.

U2 - 10.1142/S0218127415300347

DO - 10.1142/S0218127415300347

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SP - 1530034

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

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Noise Induced Jumping Dynamics between Synchronized Modes

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