Collective chaos in pulse-coupled neural networks

Olmi, Simona; Politi, Antonio; Torcini, Alessandro

doi:10.1209/0295-5075/92/60007

Cited by 127 publications

(102 citation statements)

References 31 publications

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“…In analogy with the FHN model, the introduction of a hierarchical topology in the coupling induced nested chimera states and also transitions between multi-chimera states with different multiplicities. Using a different geometrical setup of two populations of identical LIF oscillators coupled via excitatory coupling, Olmi et al studied the onset of chimeras as well as states characterized by a different degree of synchronization in the two populations [34]. Irregular synchronization phenomena have been reported for LIF elements even in the case of all-to-all connectivity [35].…”

Section: Introductionmentioning

confidence: 99%

Chimera patterns in two-dimensional networks of coupled neurons

et al. 2017

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We discuss synchronization patterns in networks of FitzHugh-Nagumo and Leaky Integrate-andFire oscillators coupled in a two-dimensional toroidal geometry. Common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes including spots, rings, stripes, and grids, observed in both models, as well as additional patterns found mainly in the FitzHughNagumo system. Both systems exhibit multistability: For the same parameter values, different initial conditions give rise to different dynamical states. Transitions occur between various patterns when the parameters (coupling range, coupling strength, refractory period, and coupling phase) are varied. Many patterns observe in the two models follow similar rules. For example the diameter of the rings grows linearly with the coupling radius.

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Section: Introductionmentioning

confidence: 99%

Chimera patterns in two-dimensional networks of coupled neurons

et al. 2017

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“…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%

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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“…They have been the subject of intensive theoretical investigations, e.g. [4][5][6][7][8][9][10][11][12][13][14][15]. Experimental evidence of chimeras has only recently been provided for optical [16], chemical [17], mechanical [18] and electronic [19] systems.…”

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confidence: 99%

Chimera Death: Symmetry Breaking in Dynamical Networks

2014

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For a network of generic oscillators with nonlocal topology and symmetry-breaking coupling we establish novel partially coherent inhomogeneous spatial patterns, which combine the features of chimera states (coexisting incongruous coherent and incoherent domains) and oscillation death (oscillation suppression), which we call chimera death. We show that due to the interplay of nonlocality and breaking of rotational symmetry by the coupling two distinct scenarios from oscillatory behavior to a stationary state regime are possible: a transition from an amplitude chimera to chimera death via in-phase synchronized oscillations, and a direct abrupt transition for larger coupling strength. Spontaneous symmetry breaking in a complex dynamical system is a fundamental and universal phenomenon which occurs in diverse fields such as physics, chemistry, and biology [1]. It implies that processes occurring in nature favor a less symmetric configuration, although the underlying principles can be symmetric. This intriguing concept has recently gained renewed interest generated by the enormous burst of works on chimera states and on oscillation death, which have emerged independently. In this Letter we draw a relation between these two.Chimera states correspond to the situation when an ensemble of identical elements self-organizes into two coexisting and spatially separated domains with dramatically different behavior, i.e., spatially coherent and incoherent oscillations [2,3]. They have been the subject of intensive theoretical investigations, e.g. [4][5][6][7][8][9][10][11][12][13][14][15]. Experimental evidence of chimeras has only recently been provided for optical [16], chemical [17], mechanical [18] and electronic [19] systems. These peculiar hybrid states may also account for the observation of partial synchrony in neural activity [20], like unihemispheric sleep, i.e., the ability of some birds or dolphins to sleep with one half of their brain while the other half remains aware [21,22]. Chimera states have been initially found for phase oscillators [2], and they typically occur in networks with nonlocal coupling. Recently, for globally coupled oscillators it has been shown that such spatio-temporal patterns can be also connected to the amplitude dynamics (amplitude-mediated chimeras) [23,24]. However, the global coupling topology does not provide a clear notion of space, which is crucial for chimera states. A further open question is whether chimeras can be extended to more general symmetry breaking states.Another fascinating effect which requires the break-up of the system's symmetry as a crucial ingredient is oscillation death which refers to stable inhomogeneous steady states (IHSS) which are created through the coupling of self-sustained oscillators. This regime occurs when a ho- * corresponding author: schoell@physik.tu-berlin.de mogeneous steady state splits into at least two distinct branches -upper and lower -which represent a newly created IHSS [25][26][27][28]. For a network of coupled elements oscillation death ...

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Collective chaos in pulse-coupled neural networks

Cited by 127 publications

References 31 publications

Chimera patterns in two-dimensional networks of coupled neurons

Chimera patterns in two-dimensional networks of coupled neurons

Chimera states in coupled Kuramoto oscillators with inertia

Chimera Death: Symmetry Breaking in Dynamical Networks

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