Chimera states in networks of type-I Morris-Lecar neurons

Çalım, Ali; Hövel, Philipp; Özer, Mahmut; Uzuntarla, Muhammet

doi:10.1103/physreve.98.062217

Cited by 51 publications

(19 citation statements)

References 80 publications

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“…White noise-induced spiral waves and multiple spatial coherence resonances in a neuronal network (M-L) with type I excitability is investigation in [32] and showed that these spiral waves could regulate the wave propagation among neurons. Ali calim et al, [33] investigated the appearance of chimera states in nonlocal networks of type-I Morris-Lecar neurons, coupled via chemical synapses and characterized chimera states in terms of firing frequency and strength of incoherence. Recently a Modified M-L model was studied [34] by blocking the target wave with artificial defects and/or partial blocking in ion channels.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation in a network of extended Morris–Lecar neurons with electromagnetic induction and its local kinetics

et al. 2020

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An extended Morris-Lecar neuron model incorporating electromagnetic flux coupling and external excitation is proposed. The complete dynamical behavior of the new model is investigated as autonomous and non-autonomous forms. Multistability and coexisting attractors are shown for the new neuron model. It is shown that when external excitation is introduced, the complete dynamical behavior of the system changes compared to the nonexcited version. To study the wave propagation pattern, we construct a network of the extended neuron model and study the generation of spiral waves under various conditions of coupling strength, stimuli parameters and system parameters. We have also studied the wave propagation pattern considering the time based chaotic-periodic neurons in the network.

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Section: Introductionmentioning

confidence: 99%

Wave propagation in a network of extended Morris–Lecar neurons with electromagnetic induction and its local kinetics

et al. 2020

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“…Chimera states were first reported in rings of non-locally and symmetrically coupled identical phase oscillators [10]. Since their discovery, they have been extensively studied both theoretically [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and experimentally [27][28][29][30][31] in a wide range of systems. For recent reviews see references [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans

Pournaki

Merfort

Ruiz

et al. 2019

Front. Appl. Math. Stat.

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We investigate synchronization patterns and chimera-like states in the modular multilayer topology of the connectome of Caenorhabditis elegans. In the special case of a designed network with two layers, one with electrical intra-community links and one with chemical inter-community links, chimera-like states are known to exist. Aiming at a more biological approach based on the actual connectivity data, we consider a network consisting of two synaptic (electrical and chemical) and one extrasynaptic (wireless) layers. Analyzing the structure and properties of this layered network using Multilayer-Louvain community detection, we identify modules whose nodes are more strongly coupled with each other than with the rest of the network. Based on this topology, we study the dynamics of coupled Hindmarsh-Rose neurons. Emerging synchronization patterns are quantified using the pairwise Euclidean distances between the values of all oscillators, locally within each community and globally across the network. We find a tendency of the wireless coupling to moderate the average coherence of the system: for stronger wireless coupling, the levels of synchronization decrease both locally and globally, and chimera-like states are not favored. By introducing an alternative method to define meaningful communities based on the dynamical correlations of the nodes, we obtain a structure that is dominated by two large communities. This promotes the emergence of chimera-like states and allows to relate the dynamics of the corresponding neurons to biological neuronal functions such as motor activities.

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“…Later, this mixed state of coherence and incoherence was termed as "chimera, " coined by Strogatz and Abrams [2]. Initially identified in a system of identical Kuramoto oscillators, the chimera state has been pinpointed in a variety of other network models such as FitzHugh-Nagumo oscillators [3,4], Rössler oscillators [5], van der Pol oscillators [6], coupled Rulkov maps [7], coupled maps [8], coupled chaotic oscillators [9], multi-layer neuronal models [10], Morris-Lecar neurons [11], modular neural network [12], neuronal network model of the cat brain [13], and data-driven model of the brain [14]. Over the years, the researchers have spotted similar fascinating chimeric patterns and labeled them as virtual chimera [15], traveling chimera [16], breathing chimera [17], spike-burst chimera states [18], and others [19,20].…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Assisted Chimera and Solitary States in Networks

et al. 2021

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Chimera and Solitary states have captivated scientists and engineers due to their peculiar dynamical states corresponding to co-existence of coherent and incoherent dynamical evolution in coupled units in various natural and artificial systems. It has been further demonstrated that such states can be engineered in systems of coupled oscillators by suitable implementation of communication delays. Here, using supervised machine learning, we predict (a) the precise value of delay which is sufficient for engineering chimera and solitary states for a given set of system's parameters, as well as (b) the intensity of incoherence for such engineered states. Ergo, using few initial data points we generate a machine learning model which can then create a more refined phase plot as well as by including new parameter values. We demonstrate our results for two different examples consisting of single layer and multi layer networks. First, the chimera states (solitary states) are engineered by establishing delays in the neighboring links of a node (the interlayer links) in a 2-D lattice (multiplex network) of oscillators. Then, different machine learning classifiers, K-nearest neighbors (KNN), support vector machine (SVM) and multi-layer perceptron neural network (MLP-NN) are employed by feeding the data obtained from the network models. Once a machine learning model is trained using the limited amount of data, it predicts the precise value of critical delay as well as the intensity of incoherence for a given unknown systems parameters values. Testing accuracy, sensitivity, and specificity analysis reveal that MLP-NN classifier is better suited than Knn or SVM classifier for the predictions of parameters values for engineered chimera and solitary states. The technique provides an easy methodology to predict critical delay values as well as intensity of incoherence for that delay value for designing an experimental setup to create solitary and chimera states.

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Chimera states in networks of type-I Morris-Lecar neurons

Cited by 51 publications

References 80 publications

Wave propagation in a network of extended Morris–Lecar neurons with electromagnetic induction and its local kinetics

Wave propagation in a network of extended Morris–Lecar neurons with electromagnetic induction and its local kinetics

Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans

Machine Learning Assisted Chimera and Solitary States in Networks

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