Abstract
Synapse coupling can benefit signal exchange between neurons and information encoding for neurons, and the collective behaviors such as synchronization and pattern selection in neuronal network are often discussed under chemical or electric synapse coupling. Electromagnetic induction is considered at molecular level when ion currents flow across the membrane and the ion concentration is fluctuated. Magnetic flux describes the effect of time-varying electromagnetic field, and memristor bridges the membrane potential and magnetic flux according to the dimensionalization requirement. Indeed, field coupling can contribute to the signal exchange between neurons by triggering superposition of electric field when synapse coupling is not available. A chain network is designed to investigate the modulation of field coupling on the collective behaviors in neuronal network connected by electric synapse between adjacent neurons. In the chain network, the contribution of field coupling from each neuron is described by introducing appropriate weight dependent on the position distance between two neurons. Statistical factor of synchronization is calculated by changing the external stimulus and weight of field coupling. It is found that the synchronization degree is dependent on the coupling intensity and weight, the synchronization, pattern selection of network connected with gap junction can be modulated by field coupling.
Highlights
Neurons are the basic structural and functional units of nervous system
It could be difficult for generic sampling and statistical analysis when network is composed of many sub-networks, but pattern selection could be effective to understand the transition in collective behaviors
The Hindmarsh-rose neuron model[59,60] mainly highlights the main nonlinear dynamic characteristics of mollusk neurons, the dynamical kinetics can be approached by the ordinary differential equations (ODEs) composed of three variables shown in ref.[59]
Summary
The Hindmarsh-rose neuron model[59,60] mainly highlights the main nonlinear dynamic characteristics of mollusk neurons, the dynamical kinetics can be approached by the ordinary differential equations (ODEs) composed of three variables shown in ref.[59]. As proposed and discussed in refs[63,64], magnetic flux is used to describe the effect of electromagnetic induction[72], and memristor is considered to realize coupling between membrane potential and magnetic flux the induction field and action potential can be bridged in physical view. The effect of electromagnetic induction and change of electric field is described by induction current. The memductance of memristor is dependent on the magnetic flux and time-varying induction current is imposed on the neuron. Distribution for synchronization factors is calculated by changing the intensity of field coupling and external stimulus. According to Eq (3), increasing the value for intensity of field coupling, positive feedback will enhance the electromagnetic induction effect, and stronger induction current will be induced to decrease the excitability of neurons. Perfect synchronization is approached when R is close to 1, and non-perfect synchronization is detected together with emergence of appropriate pattern distribution when R is close to zero
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