Intermittent chaotic chimeras for coupled rotators

Olmi, Simona; Martens, Erik Andreas; Thutupalli, Shashi; Torcini, Alessandro

doi:10.1103/physreve.92.030901

Cited by 89 publications

(63 citation statements)

References 47 publications

(80 reference statements)

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“…In particular, for sufficiently large m-values ICC solutions with broken symmetry emerges. These solutions, have been previously observed experimentally and numerically in [38] and they will be characterized in detail in Sec. V. By considering UCs, the system evolves towards chaotic solutions already at smaller inertia, namely m > 1, as shown in Fig.…”

Section: Stationary Statesmentioning

confidence: 99%

“…We proceeded as explained in Sect. II B, and as previously done in [38], in particular Λ ( * ) represents the maximum value of the probability distribution function P (Λ) (shown in the inset of Fig. 10(a)), once removed the peak around Λ = 0 characteristic of the laminar phase.…”

Section: A Finite Time Lyapunov Analysismentioning

confidence: 99%

“…In particular, the life-times of these states diverge exponentially with the system size, while their dynamics becomes regular in the thermodynamic limit. In a recent paper [38] it has been shown that a simple model of coupled oscillators with inertia (rotators) can reproduce dynamical behaviours found experimentally for two coupled populations of mechanical pendula. Starting from these results, the present paper is devoted to a detailed analysis of the collective states emerging in such model of symmetrically coupled rotators, for different inertia values and sizes.…”

Section: Introductionmentioning

confidence: 99%

“…This so-called chimera state is counter-intuitive as it appears even when the oscillators are identical, but, since its discover, this state has become a relevant subject of investigation for experimental and theoretical scientists active in different fields ranging from laser dynamics to chemical oscillators, from mechanical pendula to (computational) neuroscience. In particular chimera states have been shown to emerge in various numerical/theoretical studies [26][27][28][29][30][31][32][33][34][35] and in various experimental settings, including mechanical [36][37][38], (electro-)chemical [39][40][41] lasing systems [42,43] and BOLD fMRI signals detection during resting state activity [44], among others. Therefore chimera states are an ubiquitous phenomenon in nature much like synchronization itself and may often have been overlooked or dismissed in previous studies.…”

Section: Introductionmentioning

confidence: 99%

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Chimera states in coupled Kuramoto oscillators with inertia

Olmi

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia the system is no more chaotic and one observes mainly quasiperiodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.In 2002, simulations of abstract mathematical models revealed the existence of counterintuitive "chimera states", where an oscillator population splits into two parts, with one synchronizing and the other oscillating incoherently, even though the oscillators are identical. Since then, these counterintuitive states have become a relevant subject of investigation for experimental and theoretical scientists active in different fields, as testified by the rapidly increasing number of publications in recent years (for a review see [1, 2]). In this paper we analyze novel chimera states emerging in two symmetrically coupled populations of oscillators with inertia. In particular, the introduction of inertia allows the oscillators to synchronize via the adaptation of their own frequencies, in analogy with the mechanism observed in the firefly Pteroptix malaccae [3]. The modification of the classical Kuramoto model with the addition of an inertial term results in first order synchronization transitions and complex hysteretic phenomena [4][5][6][7][8][9]. Furthermore, networks of rotators have recently found applications in different technological contexts, including disordered arrays of Josephson junctions [10] and electrical power grids [11][12][13][14] and they could also be relevant for micro-electromechanical systems and optomechanical crystals, where chimeras and other partially disordered states likely play an important role with far reaching ramifications.

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Section: Stationary Statesmentioning

confidence: 99%

Section: A Finite Time Lyapunov Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Chimera states in coupled Kuramoto oscillators with inertia

Olmi

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Some representative ones are Refs. [48,49,50,51,52,53,54,55]. This review was entirely devoted to studies of mean-field interaction between the oscillators, namely, the case where every oscillator interacts with every other with a strength that is the same for every pair, thereby representing an extreme case of long-range interactions.…”

Section: Discussionmentioning

confidence: 99%

Spontaneous synchronisation and nonequilibrium statistical mechanics of coupled phase oscillators

Gherardini

Gupta

Ruffo

2018

Contemporary Physics

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Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously exhibit collective oscillations at a common frequency. The Kuramoto model provides the basic analytical framework to study spontaneous synchronization. The model comprises limit-cycle oscillators with distributed natural frequencies interacting through a mean-field coupling. Although more than forty years have passed since its introduction, the model continues to occupy the centre-stage of research in the field of non-linear dynamics, and is also widely applied to model diverse physical situations. In this brief review, starting with a derivation of the Kuramoto model and the synchronization phenomenon it exhibits, we summarize recent results on the study of a generalized Kuramoto model that includes inertial effects and stochastic noise. We describe the dynamics of the generalized model from a different yet a rather useful perspective, namely, that of long-range interacting systems driven out of equilibrium by quenched disordered external torques. A system is said to be long-range interacting if the inter-particle potential decays slowly as a function of distance. Using tools of statistical physics, we highlight the equilibrium and nonequilibrium aspects of the dynamics of the generalized Kuramoto model, and uncover a rather rich and complex phase diagram that it exhibits, which underlines the basic theme of intriguing emergent phenomena that are exhibited by many-body complex systems.

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Introduction

Berner

2021

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

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Intermittent chaotic chimeras for coupled rotators

Cited by 89 publications

References 47 publications

Chimera states in coupled Kuramoto oscillators with inertia

Chimera states in coupled Kuramoto oscillators with inertia

Spontaneous synchronisation and nonequilibrium statistical mechanics of coupled phase oscillators

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