Order parameter expansion and finite-size scaling study of coherent dynamics induced by quenched noise in the active rotator model

Komin, Niko; Toral, Raúl

doi:10.1103/physreve.82.051127

Cited by 7 publications

(5 citation statements)

References 29 publications

(58 reference statements)

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“…s 0 , r 0 are initial conditions of the problem. The fact that the ratio s/r satisfies the closed equation (16) which can be integrated explicitly makes it possible to reduce the order of our initial system and complete its solution. In some sense equation (18) plays the role of integral of motion (energy) in conservative systems.…”

Section: Analytical Resultsmentioning

confidence: 99%

“…When the coupling is absent (K = 0) system (1) describes the dynamics of noninteracting oscillators with a stable circular limit cycles |z j | = 1. In [10] system (1) was studied in the framework of two order parameter approximation (for more about the order parameter expansion method, see [11][12][13][14][15][16]):…”

Section: Two Order Parameter Approximationmentioning

confidence: 99%

“…In [10] system (1) was studied in the framework of two order parameter approximation (for more about the order parameter expansion method, see [11][12][13][14][15][16]):…”

Section: Two Order Parameter Approximationmentioning

confidence: 99%

See 2 more Smart Citations

Integrable order parameter dynamics of globally coupled oscillators

Pritula¹,

Prytula²,

Usatenko³

2016

J. Phys. A: Math. Theor.

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Abstract.We study the nonlinear dynamics of globally coupled nonidentical oscillators in the framework of two order parameter (mean field and amplitude-frequency correlator) reduction. The main result of the paper is the exact solution of a corresponding nonlinear system on a two-dimensional invariant manifold. We present a complete classification of phase portraits and bifurcations, obtain explicit expressions for invariant manifolds (a limit cycle among them) and derive analytical solutions for arbitrary initial data and different regimes.

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Section: Analytical Resultsmentioning

confidence: 99%

Section: Two Order Parameter Approximationmentioning

confidence: 99%

See 1 more Smart Citation

Integrable order parameter dynamics of globally coupled oscillators

Pritula¹,

Prytula²,

Usatenko³

2016

J. Phys. A: Math. Theor.

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“…This natural diversity is often referred to as quenched noise or static disorder, which makes each isolated neuron respond differently to an external forcing. It is found that the response of the neuronal ensemble to the external signal can be optimized under the right amount of quenched noise [28,29]. This finding indicates that the intrinsic diversity in neurons is important for signal detection.…”

Section: Introductionmentioning

confidence: 87%

Effect of initial phase diversity on signal detection in excitable systems

Liang

Liu

2016

Sci. China Technol. Sci.

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Undoubtedly, the sensory organs of biological systems have been evolved to accurately detect and locate the external stimuli, even if they are very weak. However, the mechanism underlying this ability is still not fully understood. Previously, it had been shown that stochastic resonance may be a good candidate to explain this ability, by which the response of a system to an external signal is amplified by the presence of noise. Recently, it is pointed out that the initial phase diversity in external signals can be also served as a simple and feasible mechanism for weak signal detection or amplification in excitable neurons. We here make a brief review on this progress. We will show that there are two kinds of effects of initial phase diversity: one is the phase disorder, i.e., the initial phases are different and static, and the other is the phase noise, i.e., the initial phases are time-varying like noise. Both cases show that initial phase diversity in subthreshold periodic signals can indeed play a constructive role in the emergence of sustained spiking activity. As initial phase diversity can mimic different arrival times from source signal to sensory organs, these findings may provide a cue for understanding the hunting behaviors of some biological systems.stochastic resonance, excitable neuron, phase noise, subthreshold signal Citation:Liang X M, Liu Z H. Effect of initial phase diversity on signal detection in excitable systems.

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“…The influence of the first type effects have been intensevely studied in recent years (e.g., see [28][29][30]). Actually, the modifications of the second type have been also considered in the literature [31][32][33]. In this work, we assume, that both effects are present and play an important role.…”

Section: Introductionmentioning

confidence: 99%

Symmetry broken states in an ensemble of globally coupled pendulums

Bolotov

Munyaev

Smirnov

et al. 2020

Physica D: Nonlinear Phenomena

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We consider the rotational dynamics in an ensemble of identical globally coupled pendulums. This model is essentially a generalization of the standard Kuramoto model, which takes into account the inertia and the intrinsic nonlinearity of the community elements. There exist the wide variety of inphase and out-of-phase regimes. Many of these states appear due to instability of in-phase rotational mode that leads to partially broken symmetry in the considered model. Our theoretical analysis allows one to find the boundaries of the instability domain for ensembles with arbitrary number of pendulums. In the case of three elements, for system control parameter sets corresponding to the unstable in-phase rotations we numerically find a number of out-of-phase rotation modes and study in detail their stability and bifurcations. We demonstrate that chaotic behavior arises throw the cascade period doubling bifurcations and torus destruction. As a result, we obtain a sufficiently detailed picture of the symmetry breaking and existence of various regular and chaotic states in an ensemble of identical globally coupled pendulums. In particular, we show that the family of symmetry-broken states includes chimera attractors. In these regimes, one part of the oscillators moving irregularly is synchronized, and the other pendulums rotate separately. We directly demonstrate the example of chimera states in the system under discussion for the cases of three and four number of elements.PACS numbers: 05.45.Xt, 45.20.dc

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Order parameter expansion and finite-size scaling study of coherent dynamics induced by quenched noise in the active rotator model

Cited by 7 publications

References 29 publications

Integrable order parameter dynamics of globally coupled oscillators

Integrable order parameter dynamics of globally coupled oscillators

Effect of initial phase diversity on signal detection in excitable systems

Symmetry broken states in an ensemble of globally coupled pendulums

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