Chimera patterns induced by distance-dependent power-law coupling in ecological networks

Banerjee, Tanmoy; Dutta, Partha Sharathi; Zakharova, Anna; Schöll, Eckehard

doi:10.1103/physreve.94.032206

Cited by 93 publications

(45 citation statements)

References 64 publications

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“…Chimera states arise surprisingly in networks of completely identical units and symmetric coupling topologies 2,4,7 . Initially detected for nonlocally coupled rings of phase oscillators, these hybrid patterns have been found for various other systems and network structures ranging from globally coupled networks [8][9][10] and networks with power-law coupling 11 to irregular topologies [12][13][14][15][16] and hierarchical, quasi-fractal connectivities [17][18][19][20][21][22] . Solitary states have been reported for local, nonlocal and global types of coupling in networks of Kuramoto oscillators with inertia 6,23 .…”

Section: Introductionmentioning

confidence: 95%

Weak multiplexing in neural networks: Switching between chimera and solitary states

Mikhaylenko

Ramlow

Jalan

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate spatio-temporal patterns occurring in a two-layer multiplex network of oscillatory FitzHugh-Nagumo neurons, where each layer is represented by a nonlocally coupled ring. We show that weak multiplexing, i.e., when the coupling between the layers is smaller than that within the layers, can have a significant impact on the dynamics of the neural network. We develop control strategies based on weak multiplexing and demonstrate how the desired state in one layer can be achieved without manipulating its parameters, but only by adjusting the other layer. We find that for coupling range mismatch weak multiplexing leads to the appearance of chimera states with different shapes of the mean velocity profile for parameter ranges where they do not exist in isolation. Moreover, we show that introducing a coupling strength mismatch between the layers can suppress chimera states with one incoherent domain (one-headed chimeras) and induce various other regimes such as in-phase synchronization or two-headed chimeras. Interestingly, small intra-layer coupling strength mismatch allows to achieve solitary states throughout the whole network.In nonlinear dynamics the paradigmatic FitzHugh-Nagumo (FHN) system is used to model the behavior of neurons. A single-layer network of nonlocally coupled oscillatory FHN neurons demonstrates various dynamic regimes including chimera states, that represent an intriguing mechanism of transition from complete coherence to complete incoherence. Here, we focus on a two-layer multiplex network and develop the tools for controlling the spatio-temporal patterns in the presence of weak coupling between the layers, i.e. weak multiplexing. We show that multiplexing combined with a mismatch between the layers, allows to induce chimera states in networks, where they do not appear in isolation. Our control also works in the opposite direction leading to the suppression of chimera states. Interestingly, small mismatch in the intra-layer coupling strength results in the formation of solitary states, that offer, compared to chimera states, an alternative scenario of transition from coherence to incoherence. Since multilayer structures naturally occur in neural networks (e.g., brain networks), we expect that our results can be useful for understanding and controlling of biological networks.

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Section: Introductionmentioning

confidence: 95%

Weak multiplexing in neural networks: Switching between chimera and solitary states

Mikhaylenko

Ramlow

Jalan

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…[3][4][5][6][7][8][9] The interest in the study of this fascinating phenomenon grew thanks to the observation of chimeras in experiments 5,[10][11][12][13][14][15][16] and numerous conceptual links established between chimera states on one hand and natural and man-made phenomena on the other. [17][18][19][20][21] Many advances were made in the understanding chimeras from a mathematical perspective (see Ref. 22 and references therein).…”

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confidence: 99%

Controlling chimera states via minimal coupling modification

Ruzzene

Omelchenko

Schöll

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We propose a method to control chimera states in a ring-shaped network of nonlocally coupled phase oscillators. This method acts exclusively on the network's connectivity. Using the idea of a pacemaker oscillator we investigate which is the minimal action needed to control chimeras. We implement the pacemaker choosing one oscillator and making its links unidirectional. Our results show that a pacemaker induces chimeras for parameters and initial conditions for which they do not form spontaneously. Furthermore, the pacemaker attracts the incoherent part of the chimera state, thus controlling its position. Beyond that, we find that these control effects can be achieved with modifications of the network's connectivity that are less invasive than a pacemaker. Namely the minimal action of just modifying the strength of one connection allows one to control chimeras.

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“…Another example of a chimera pattern where coherence (incoherence) corresponds to order (disorder) in space, but there are no oscillations in time, is chimera death, i.e., a steady state chimera pattern found for nonlocal [14] and mean-field diffusive coupling [16]. Recently, a chimera state which combines synchronized oscillations and steady states coexisting in space has been reported [17,18]. Amplitude chimeras and chimera death emerge in networks with symmetry-breaking coupling, which is a crucial condition for the emergence of non-trivial steady states (oscillation death) [19].…”

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Stability of amplitude chimeras in oscillator networks

Tumash¹,

Zakharova²,

Lehnert³

et al. 2017

EPL

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-We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of coherent and of incoherent oscillations. We calculate the Floquet exponents and the corresponding eigenvectors in dependence upon the coupling strength and range, and discuss the implications for the phase space structure. The existence of at least one positive real part of the Floquet exponents indicates an unstable manifold in phase space, which explains the nature of these states as long-living transients. Additionally, we find a Stuart-Landau network of minimum size N = 12 exhibiting amplitude chimeras.Introduction. -The dynamical state of networks of homogeneously coupled identical elements can show a peculiar behavior by self-organizing into two spatially separated domains with dramatically different behavior, e.g. a spatially coherent and a spatially incoherent region. This phenomenon was named chimera state by Abrams and Strogatz [1] after the Greek fire-breathing monster, whose body consists of different animals. These hybrid states were discovered for phase oscillators in the early 2000's by Kuramoto and Battogtokh [2]. They observed a spontaneous breakup of the system into spatially coexisting synchronized and desynchronized domains with respect to the phase.Chimera states have possible applications to neural activity [3,4], heart fibrillation [5] and social systems [6]. Chimera states were also associated with such phenomena as epileptic seizure [7] and unihemispheric sleep, which has been detected for some sea mammals and birds [8]. These creatures can sleep with only one half of their brain while the other half remains awake. For instance, this enables sleeping dolphins to detect predators and migrant birds can travel for hundreds of kilometers without having a break [9]. Recently, unihemispheric sleep has been found also for humans [10].Chimera states were initially found for coupled phase oscillators, where coherence is related to phase-and frequency-locked oscillators and incoherence is associated with drifting oscillators. Since then numerous chimera

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Chimera patterns induced by distance-dependent power-law coupling in ecological networks

Cited by 93 publications

References 64 publications

Weak multiplexing in neural networks: Switching between chimera and solitary states

Weak multiplexing in neural networks: Switching between chimera and solitary states

Controlling chimera states via minimal coupling modification

Stability of amplitude chimeras in oscillator networks

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