Abstract
Autapse plays an important role in regulating the electric activity of neuron by feedbacking time-delayed current on the membrane of neuron. Autapses are considered in a local area of regular network of neurons to investigate the development of spatiotemporal pattern, and emergence of spiral wave is observed while it fails to grow up and occupy the network completely. It is found that spiral wave can be induced to occupy more area in the network under optimized noise on the network with periodical or no-flux boundary condition being used. The developed spiral wave with self-sustained property can regulate the collective behaviors of neurons as a pacemaker. To detect the collective behaviors, a statistical factor of synchronization is calculated to investigate the emergence of ordered state in the network. The network keeps ordered state when self-sustained spiral wave is formed under noise and autapse in local area of network, and it independent of the selection of periodical or no-flux boundary condition. The developed stable spiral wave could be helpful for memory due to the distinct self-sustained property.
Highlights
Neuronal system consists of a large number of neurons, and the collective electric activities of neurons can emerge complex spatiotemporal patterns during the process of signals
It was reported that spiral wave can be found in the cortex of brain [20222], and some theoretical investigations [23,24] have been presented to explore the potential formation mechanism of spiral wave and multi-armed spiral wave in the network of neurons, these results [24] have confirmed that intermediate channels blocking in neurons in a local area of neuronal network can induce emergence of spiral wave, and the stability of multiarmed spiral wave was discussed
In mathematical models and computer simulations, periodic boundary conditions (PBC) are a set of boundary conditions that are often used to simulate a large system by modeling a small part that is far from its edge
Summary
Neuronal system consists of a large number of neurons, and the collective electric activities of neurons can emerge complex spatiotemporal patterns during the process of signals. Is there any new ‘pacemaker’ in a two-dimensional array network induced by the distribution of electric autapses the collective behaviors of neurons can be regulated? A regular network of Hindmarsh-Rose neuron is designed in a two-dimensional array, some autapses are introduced into the neurons in a local area and noise is considered on the whole network. A statistical function is defined to detect the transition of spiral wave under noise and autapses in a local area of the network. Breakup and development of spiral wave in the network induced by few autapses, and the effect of noise will be investigated, respectively. Negative values will be selected for gain g to detect the development of spiral wave in the network induced by noise and a fraction of electric autapses in a local area of the network. To detect the transition of collective behaviors of neurons in the network, a statistical factor of synchronization in a two-dimensional space is defined according to mean filed theory, and the factor of synchronization R is described by [18,27,47]
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