Finite Size Effects in Networks of Coupled Neurons

Tsigkri-DeSmedt, N. D.; Vlamos, Panayiotis; Provata, A.

doi:10.1007/978-3-030-32622-7_37

Cited by 2 publications

(2 citation statements)

References 35 publications

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“…Therefore, a number of nodes of the order of 500 for each ring covers adequately the computational brain division. 2 From previous studies of the LIF and FitzHugh Nagumo networks we have seen that a number of 500-1000 nodes is good enough to avoid finite size effects which are dominant in smaller sizes (Tsigkri-DeSmedt et al, 2020).…”

Section: Synchronization Patterns For Positive Inter-ring Couplingmentioning

confidence: 99%

Synchronization in Multiplex Leaky Integrate-and-Fire Networks With Nonlocal Interactions

Anesiadis

Provata

2022

Front. Netw. Physiol.

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We study synchronization phenomena in a multiplex network composed of two rings with identical Leaky Integrate-and-Fire (LIF) oscillators located on the nodes of the rings. Within each ring the LIF oscillators interact nonlocally, while between rings there are one-to-one inter-ring interactions. This structure is motivated by the observed connectivity between the two hemispheres of the brain: within each hemisphere the various brain regions interact with neighboring regions, while across hemispheres each region interacts, primarily, with the functionally homologous region. We consider both positive (excitatory) and negative (inhibitory) linking. We identify numerically various parameter regimes where the multiplex network develops coexistence of active and subthreshold domains, chimera states, solitary states, full coherence or incoherence. In particular, for weak inter-ring coupling (weak multiplexing) different synchronization patterns on the two rings are supported. These are stable and are obtained when the intra-ring coupling values are near the critical points separating qualitatively distinct synchronization regimes, e.g., between the travelling fronts regime and the chimera state one.

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Section: Synchronization Patterns For Positive Inter-ring Couplingmentioning

confidence: 99%

Synchronization in Multiplex Leaky Integrate-and-Fire Networks With Nonlocal Interactions

Anesiadis

Provata

2022

Front. Netw. Physiol.

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“…In this work Kuramoto and Battogtokh used the phase oscillator to assimilate the behavior of neurons. Later on, chimera states were found in other neuronal models, such as in the FitzHugh-Nagumo [2][3][4], Hindmarsh-Rose [5,6], Van der Pol [7] and in the Leaky Integrate-and-Fire (LIF) models [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Controlling the Chimera Form in the Leaky Integrate-and-Fire Model

2021

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We study the influence of broken connectivity and frequency disorder in systems of coupled neuronal oscillators. Under nonlocal coupling, systems of nonlinear oscillators, such as Kuramoto, FitzHugh-Nagumo or Integrate-and-Fire oscillators, demonstrate nontrivial synchronization patterns. One of these patterns is the "chimera state", which consists of coexisting coherent and incoherent domains. In networks of biological neurons, the connectivity is not always perfect, but might be locally broken, or interrupted due to pathologies, neuron degenerative disorders or accidents. Our simulations show that destructed connectivity drastically affects synchronization, driving the coherent parts of the chimera state to cover symmetrically the region where the anomaly is located. The network synchronization decreases with the size of the destructed region as evidenced by the Kuramoto synchronization index. To the contrary, when keeping the connectivity of all nodes intact, altering the frequency in a block of oscillators drives the incoherent part of the chimera state toward the anomaly. This work is in-line with recent dynamical approaches aiming to locate anomalies in the structure of brain networks, in particular when the anomalies have small, difficult-to-detect sizes.

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Finite Size Effects in Networks of Coupled Neurons

Cited by 2 publications

References 35 publications

Synchronization in Multiplex Leaky Integrate-and-Fire Networks With Nonlocal Interactions

Synchronization in Multiplex Leaky Integrate-and-Fire Networks With Nonlocal Interactions

Controlling the Chimera Form in the Leaky Integrate-and-Fire Model

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