Spike-burst chimera states in an adaptive exponential integrate-and-fire neuronal network

Santos, Miguel Ángel; Protachevicz, Paulo R.; Iarosz, Kelly C.; Caldas, Iberê L.; Viana, Ricardo L.; Borges, Fernando S.; Ren, Hai‐Peng; Szezech, José D.; Batista, Antônio M.; Grebogi, Celso

doi:10.1063/1.5087129

Cited by 25 publications

(13 citation statements)

References 38 publications

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“…These findings could in the future influence the developments of control strategies for epileptic seizures which have recently been related to the collapse of chimera states [40]. Furthermore, the results presented in this study improve the general understanding of the mechanism and control of the transition towards the synchronized or coherent state, which may play a role in many real-life systems [15][16][17]19,20,22,23] where chimera states were found and controlling them could become relevant in future applications. In a broad perspective, the emergence of spontaneous synchronization plays a fundamental role, e.g., in dissimilar silicon nitride micromechanical oscillators [41], where the authors suggest a new class of FIG.…”

Section: Discussionmentioning

confidence: 53%

“…In this study we discuss the dynamics of chimera states, defined by the coexistence of spatial regions with coherent and incoherent dynamics. They can be found in many reallife systems, like in superconducting quantum interference devices (SQUIDS) [15,16], the cognitive organization of the brain [17,18], in biological systems like self-propelled particles [19], or neural networks [20,21]. In addition, chimera states were found in quantum mechanics [22] or mechanical oscillators [23].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 53%

Section: Introductionmentioning

confidence: 99%

Susceptibility of transient chimera states

Lilienkamp

Parlitz

2020

Phys. Rev. E

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“…Additionaly, σ i and σ are the variance of each neuron's voltage and the averaged voltage of the whole network, respectively. In equations (10) and (11), • denotes the time average. Then the synchrony measure S is defined as equation (12).…”

Section: Measurementmentioning

confidence: 99%

“…In the past few decades, there have been various techniques used to concern the synchronization of neuronal networks [10]- [13]. On one hand, some scholars have studied how the external time periodic stimulation affected the neuronal synchronization in the brain [14].…”

Section: Introductionmentioning

confidence: 99%

Synchronization and Rhythm Transition in a Complex Neuronal Network

et al. 2020

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Synchronization and rhythm transition in an excitatory-inhibitory balanced cortical neuronal network are investigated in this paper. A small-world neuronal network is performed to be the cortical region of cerebral cortex, which is composed of different types of Izhikevich neurons. The combination of regular spiking (RS) cells, chattering (CH) cells, or mixed RS and CH cells are imitated as excitatory neurons, whereas fast spiking (FS) cells mimic inhibitory neurons. We mainly focus on the effect of different types of neurons on synchronization and rhythm transition of the neuronal network. The simulation results illustrate that it is easier for the neuronal network with CH excitatory neurons to achieve synchronization, and it is also more susceptible to the parameters than the network with RS neurons. Together with the weight of the synaptic connection, the structure of the small-world network is also explored to identify its influence on the synchronization and the rhythm transition. Moreover, we found that the synchronization performance could be improved by increasing the degree of influence among neurons. Importantly, the synchronization states are associated with the rhythm transitions. Especially, the consistency of synchronization of the neuronal network and γ band rhythm is illustrated. In addition, our results could have an important significance on further understanding brain rhythms and synchrony in neuroscience.

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“…In this work, we study AEIF neurons randomly connected by means of excitatory and inhibitory conductivities. The neurons can exhibit not only spike but also burst activities (Santos et al, 2019 ). Our results show that the delayed conductance in both excitatory and inhibitory connections play an important role in the neuronal synchronization.…”

Section: Introductionmentioning

confidence: 99%