Optimal phase description of chaotic oscillators

Schwabedal, Justus T. C.; Pikovsky, Arkady; Kralemann, Björn; Rosenblum, Michael

doi:10.1103/physreve.85.026216

Cited by 28 publications

(24 citation statements)

References 21 publications

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“…Nevertheless, methods that allow one to effectively reduce the influence of these and other confounding variables are still missing. It remains to be shown whether recently proposed methods for an improved phase extraction 78,79 or specifically designed surrogate techniques can be of help to better delineate functional from spurious interactions between dynamical systems.…”

Section: Resultsmentioning

confidence: 99%

Can spurious indications for phase synchronization due to superimposed signals be avoided?

Porz

Kiel

Lehnertz

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate the relative merit of phase-based methods-mean phase coherence, unweighted and weighted phase lag index-for estimating the strength of interactions between dynamical systems from empirical time series which are affected by common sources and noise. By numerically analyzing the interaction dynamics of coupled model systems, we compare these methods to each other with respect to their ability to distinguish between different levels of coupling for various simulated experimental situations. We complement our numerical studies by investigating consistency and temporal variations of the strength of interactions within and between brain regions using intracranial electroencephalographic recordings from an epilepsy patient. Our findings indicate that the unweighted and weighted phase lag index are less prone to the influence of common sources but that this advantage may lead to constrictions limiting the applicability of these methods.

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Section: Resultsmentioning

confidence: 99%

Can spurious indications for phase synchronization due to superimposed signals be avoided?

Porz

Kiel

Lehnertz

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Finally, we emphasize that our corresponding considerations are closely related to the problem of finding an optimal phase definition for a chaotic system. [80][81][82][83][84] Achieving a better understanding of the linkage between both geometric and optimal phase approaches will be a subject of future research. …”

Section: -11mentioning

confidence: 99%

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Zou

Donner

Wickramasinghe

et al. 2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Chaotic attractors are known to often exhibit not only complex dynamics but also a complex geometry in phase space. In this work, we provide a detailed characterization of chaotic electrochemical oscillations obtained experimentally as well as numerically from a corresponding mathematical model. Power spectral density and recurrence time distributions reveal a considerable increase of dynamic complexity with increasing temperature of the system, resulting in a larger relative spread of the attractor in phase space. By allowing for feasible coordinate transformations, we demonstrate that the system, however, remains phase-coherent over the whole considered parameter range. This finding motivates a critical review of existing definitions of phase coherence that are exclusively based on dynamical characteristics and are thus potentially sensitive to projection effects in phase space. In contrast, referring to the attractor geometry, the gradual changes in some fundamental properties of the system commonly related to its phase coherence can be alternatively studied from a purely structural point of view. As a prospective example for a corresponding framework, recurrence network analysis widely avoids undesired projection effects that otherwise can lead to ambiguous results of some existing approaches to studying phase coherence. Our corresponding results demonstrate that since temperature increase induces more complex chaotic chemical reactions, the recurrence network properties describing attractor geometry also change gradually: the bimodality of the distribution of local clustering coefficients due to the attractor’s band structure disappears, and the corresponding asymmetry of the distribution as well as the average path length increase.

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“…Many chaotic attractors allow a representation in terms of amplitudes and phases [3,15,16], but because the phase generally performs a chaos-induced diffusion, isophases in the strict sense do not exist. Recently, description of chaotic oscillations in terms of approximate isophases has been suggested [17]. With noise, the return times to a Poincaré surface of a strange attractor can be defined in the averaged sense only, and in this respect there is no difference between chaotic and regular deterministic oscillators.…”

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confidence: 99%

Phase Description of Stochastic Oscillations

Schwabedal

Pikovsky

2013

Phys. Rev. Lett.

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We introduce an invariant phase description of stochastic oscillations by generalizing the concept of standard isophases. The average isophases are constructed as sections in the state space, having a constant mean first return time. The approach allows to obtain a global phase variable of noisy oscillations, even in the cases where the phase is ill-defined in the deterministic limit. A simple numerical method for finding the isophases is illustrated for noise-induced switching between two coexisting limit cycles, and for noise-induced oscillation in an excitable system. We also discuss how to determine the isophases for experimentally observed irregular oscillations, providing a basis for a refined phase description of observed oscillatory dynamics.

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Optimal phase description of chaotic oscillators

Cited by 28 publications

References 21 publications

Can spurious indications for phase synchronization due to superimposed signals be avoided?

Can spurious indications for phase synchronization due to superimposed signals be avoided?

Phase coherence and attractor geometry of chaotic electrochemical oscillators

Phase Description of Stochastic Oscillations

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