The influence of connectivity on the firing rate in a neuronal network with electrical and chemical synapses

Abstract-We study the firing rate in a model of cellular automaton for a neural network with electrical and chemical synapses. We proposed a model in which local connections in the network represent electrical synapses and the nonlocal simulate the chemical synapses. The non-local connections or shortcuts were inserted according to the model of complex network small world with a probability specified connection, also being possible to add a time delay in the simulations. The time delay is the time required to update the state variable of a neuron affected. The mechanism provides chemical synapses to conduct self-sustained neuronal firing, which can be periodic or not, depending on the insertion of the time delay. Considering only the electrical synapses, the dynamics of neuronal firing rapidly decays to zero.Keywords-Neurodynamics, Neural Networks, cellular automaton.Resumo-Estudamos a taxa de disparos em um modelo de autômato celular para uma rede neural com sinapses elétricas e químicas. Foi proposto um modelo em que as conexões locais na rede representam as sinapses elétricas e, as não locais simulam as sinapses químicas. As conexões não locais ou atalhos foram inseridos de acordo com o modelo de rede complexa mundo pequeno com uma probabilidade de conexão especificada, também sendo possível a adição de um tempo de atraso nas simulações. O tempo de atraso representa o intervalo de tempo necessário para atualizar a variável de estado de um neurônio afetado. O mecanismo com sinapses químicas fornece um comportamento auto-sustentável de disparos neuronais, que pode ser periódico ou não, dependendo da inserção do tempo de atraso. Considerando somente as sinapses elétricas, a dinâmica de disparos decai rapidamente a zero.

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“…Neste caso não foi considerado estímulos ou pertubações externas. Portanto a variável h i será dada por (Iarosz et al, 2012):…”

Section: Dinâmica Não Local: Inclusão De Sinapses Químicasunclassified

Taxa de disparos em uma rede neural modelada por autômato celular

Borges¹,

Iarosz²,

Batista³

et al. 2013

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…Many applications of single-neuron models already exist, but it seems that a systematic study of their response as a function of the control parameters lack. Map-based models are easier to treat and analyze and have been used to describe specific situations, especially when considering coupled elements characterized by chemical [28,29], electrical [30,31] or both aspects [32][33][34][35]. The topology of neural networks is also an essential player in their dynamical behavior, as reported for, e.g., scalefree [32], global [36], mean-field [37], small world [38], and Apollonian [39,40] networks.…”

Section: Introductionmentioning

confidence: 99%

Distribution of spiking and bursting in Rulkov’s neuron model

Ramírez-Ávila

Depickère

Jánosi

et al. 2022

Eur. Phys. J. Spec. Top.

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Large-scale brain simulations require the investigation of large networks of realistic neuron models, usually represented by sets of differential equations. Here we report a detailed fine-scale study of the dynamical response over extended parameter ranges of a computationally inexpensive model, the two-dimensional Rulkov map, which reproduces well the spiking and spiking-bursting activity of real biological neurons. In addition, we provide evidence of the existence of nested arithmetic progressions among periodic pulsing and bursting phases of Rulkov’s neuron. We find that specific remarkably complex nested sequences of periodic neural oscillations can be expressed as simple linear combinations of pairs of certain basal periodicities. Moreover, such nested progressions are robust and can be observed abundantly in diverse control parameter planes which are described in detail. We believe such findings to add significantly to the knowledge of Rulkov neuron dynamics and to be potentially helpful in large-scale simulations of the brain and other complex neuron networks.

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“…The DR of a neuronal network increases with the network size until it reaches a saturation value [11]. The increase of the DR value is also associated with the increase of the number of excitatory chemical synapses [12,13]. Borges et al [14] reported the complementary effect of chemical and electrical synapses on the enhance of the DR. Protachevicz et al shown that chemical synapses can enhance DR of the neural network submitted to external stimuli [15].…”

Section: Introductionmentioning

confidence: 99%

Influence of inhibitory synapses on the criticality of excitable neuronal networks

Borges¹,

Protachevicz²,

Santos³

et al. 2020

Preprint

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In this work, we study the dynamic range of a neuronal network of excitable neurons with excitatory and inhibitory synapses. We obtain an analytical expression for the critical point as a function of the excitatory and inhibitory synaptic intensities. We also determine an analytical expression that gives the critical point value in which the maximal dynamic range occurs. Depending on the mean connection degree and coupling weights, the critical points can exhibit ceasing or ceaseless dynamics. However, the dynamic range is equal in both cases. We observe that the external stimulus mask some effects of self-sustained activity (ceaseless dynamic) in the region where the dynamic range is calculated. In these regions, the firing rate is the same for ceaseless dynamics and ceasing activity. Furthermore, we verify that excitatory and inhibitory inputs are approximately equal for a network with a large number of connections, showing excitatory-inhibitory balance as reported experimentally.

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The influence of connectivity on the firing rate in a neuronal network with electrical and chemical synapses

Cited by 8 publications

References 45 publications

Taxa de disparos em uma rede neural modelada por autômato celular

Taxa de disparos em uma rede neural modelada por autômato celular

Distribution of spiking and bursting in Rulkov’s neuron model

Influence of inhibitory synapses on the criticality of excitable neuronal networks

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