Controlling chimera states via minimal coupling modification

Ruzzene, Giulia; Omelchenko, Iryna; Schöll, Eckehard; Zakharova, Anna; Andrzejak, Ralph G.

doi:10.1063/1.5097570

Cited by 20 publications

(18 citation statements)

References 37 publications

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“…where i is the imaginary unit, δ determines the number of neighbours of one oscillator used to calculate its local order parameter and I is the time average over the evaluation interval I. As control mechanism, we use a pacemaker oscillator [68] in one or both layers. A pacemaker is an oscillator which is not receiving any input from the rest of the network but is sending output like all the others.…”

Section: B Control Impactmentioning

confidence: 99%

“…Furthermore, the initial position of the two groups is sensitively dependent on the initial conditions. The control of these instabilities of chimera states has been the subject of several studies which considered single-layer networks of various types of oscillators [61][62][63][64][65][66][67][68]. In contrast, control of chimera states in multilayer networks is still widely unexplored.…”

Section: Introductionmentioning

confidence: 99%

“…It is therefore natural to ask whether other mechanisms to control chimera states may be effective in multilayer networks. Here we propose a method based on the interplay of a pacemaker oscillator [68] and the multiplex structure. Advantages of our method include its simple implementation and the fact that it does not require any feedback from the system.…”

Section: Introductionmentioning

confidence: 99%

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Remote pacemaker control of chimera states in multilayer networks of neurons

et al. 2020

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Networks of coupled nonlinear oscillators allow for the formation of nontrivial partially synchronized spatiotemporal patterns, such as chimera states, in which there are coexisting coherent (synchronized) and incoherent (desynchronized) domains. These complementary domains form spontaneously and it is impossible to predict where the synchronized group will be positioned within the network. Therefore, possible ways to control the spatial position of the coherent and incoherent groups forming the chimera states are of high current interest. In this work we investigate how to control chimera patterns in multiplex networks of FitzHugh-Nagumo neurons, and in particular we want to prove that it is possible to remotely control chimera states exploiting the multiplex structure. We introduce a pacemaker oscillator within the network: this is an oscillator that does not receive input from the rest of the network but is sending out information to its neighbours. The pacemakers can be positioned in one or both layers. Their presence breaks the spatial symmetry of the layer in which they are introduced and allows us to control the position of the incoherent domain. We demonstrate how the remote control is possible for both uni-and bidirectional coupling between the layers. Furthermore we show which are the limitations of our control mechanisms when it is generalized from single layer to multilayer networks.

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Section: B Control Impactmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Remote pacemaker control of chimera states in multilayer networks of neurons

et al. 2020

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“…We have seen that by increasing the size of the system, e.g., from 81 × 81 to 243 × 243, it is possible to stabilize multichimera states, even for stochastic fractal connectivity. Apart from increasing the system size, other ways of pinning the traveling patterns (see e.g., Isele et al [58] and Ruzzene et al [59]) could be used in order to clarify the presence of hierarchical patterns in the ω− profile within the incoherent domains.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

Chimera States With 2D Deterministic and Random Fractal Connectivity

Argyropoulos

Provata

2019

Front. Appl. Math. Stat.

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We study the formation of chimera states in 2D lattices with hierarchical (fractal) connectivity. The dynamics of the nodes follow the Leaky Integrate-and-Fire model and the connectivity has the form of a deterministic or a random Sierpinski carpet. We provide numerical evidence that for deterministic fractal connectivity and small values of the coupling strength, a hierarchical incoherent spot is produced with internal structure influenced by the fractal connectivity scheme. The spot size is similar to the size of the coupling matrix. Stable spots can be formed for symmetric fractal connectivity, while traveling ones are found when the connectivity matrix is asymmetric with respect to the center. For fractal coupling schemes spiral wave chimeras are produced and curious stable patterns are reported, which present triple coexistence of coherent regions, incoherent domains and traveling waves. In all cases, the coherent domains demonstrate the lowest mean phase velocities ω, the incoherent domains show intermediate ω-velocities, while the traveling waves show the highest ω-values. These findings confirm previous studies on symmetric deterministic hierarchical connectivities and extend here to slanted and random fractals.

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“…However, with the relation mentioned above we suggest in this study regions of the chimera state where small but finite perturbations will most likely cause a prevention of the upcoming self-termination, if it is close to the collapse. The localized (in space and time) application of a finite perturbation is therefore in contrast to former control strategies of chimera states, which mostly rely on feedback control or other (global) approaches [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Susceptibility of transient chimera states

Lilienkamp

Parlitz

2020

Phys. Rev. E

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Chaotic dynamics of a dynamical system is not necessarily persistent. If there is (without any active intervention from outside) a transition towards a (possibly nonchaotic) attractor, this phenomenon is called transient chaos, which can be observed in a variety of systems, e.g., in chemical reactions, population dynamics, neuronal activity, or cardiac dynamics. Also, chimera states, which show coherent and incoherent dynamics in spatially distinct regions of the system, are often chaotic transients. In many practical cases, the control of the chaotic dynamics (either the termination or the preservation of the chaotic dynamics) is desired. Although the self-termination typically occurs quite abruptly and can so far in general not be properly predicted, previous studies showed that in many systems a 'terminal transient phase" (TTP) prior to the self-termination existed, where the system was less susceptible against small but finite perturbations in different directions in state space. In this study, we show that, in the specific case of chimera states, these susceptible directions can be related to the structure of the chimera, which we divide into the coherent part, the incoherent part and the boundary in between. That means, in practice, if self-termination is close we can identify the direction of perturbation which is likely to maintain the chaotic dynamics (the chimera state). This finding improves the general understanding of the state space structure during the TTP, and could contribute also to practical applications like future control strategies of epileptic seizures which have been recently related to the collapse of chimera states.

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Controlling chimera states via minimal coupling modification

Cited by 20 publications

References 37 publications

Remote pacemaker control of chimera states in multilayer networks of neurons

Remote pacemaker control of chimera states in multilayer networks of neurons

Chimera States With 2D Deterministic and Random Fractal Connectivity

Susceptibility of transient chimera states

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