Synchronization control of field-coupled neurons with distributed time delays
School of Mathematics and Physics, Lanzhou Jiaotong University, 730070, Lanzhou, China
2 College of Electrical and Information Engineering, Lanzhou University of Technology, 730050, Lanzhou, China
3 School of Physics and Electromechanical Engineering, Hexi University, 734000, Zhangye, China
Accepted: 5 December 2022
Published online: 21 December 2022
Electrical synapses can quickly activate the gap junctions between adjacent neurons, so the effect of electrical synaptic coupling is often equivalent to that of voltage coupling based on resistors; the release of neurotransmitters in chemical synapses can cause the pumping of ions, which in turn excites electromagnetic fields inside and outside the cell, so chemical synapses can be described by field coupling based on inductance coils. In this paper, resistor and inductor are employed to connect two HR neurons in order to describe the coupling effects of electrical synaptic and chemical synaptic in the actual neuronal network, respectively. Moreover, distributed time delays are introduced into the coupling terms when taking into account that the propagation of neuronal signal is non-instantaneous and non-uniform. For the resistor-coupled and inductor-coupled neuron models containing weak and strong kernel functions, the effects of synaptic coupling enhance on synchronization behavior and the bifurcation structures are compared among the three control modes (without control, using Lyapunov control and using back-stepping control). Then synchronization, approximate synchronization and asynchronization behaviors are revealed, and it is confirmed that the implementation of synchronization and bifurcation patterns of coupled neurons depend on the selections of coupling channels and kernel functions. Finally, the optimal control method, that is the back-stepping control method is evaluated in terms of controller design, synchronization error and synchronization range. From a physical point of view, the involvement of resistor coupling explains the contribution of coupled electrical synapses through the activation of gap connections, while inductor coupling provides the modulation of chemical synapses through the pumping and transmission of energy by time-varying electromagnetic fields triggered by time-varying currents. The activation and regulation between coupling channels can provide some clues to identify the diversity of synaptic function and synaptic plasticity.
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