Bifurcation Analysis and Synchronous Patterns between Field Coupled Neurons with Time Delay

Abstract

Neurons encode and transmit signals through chemical synaptic or electrical synaptic connections in the actual nervous system. Exploring the biophysical properties of coupling channels is of great significance for further understanding the rhythm transitions of neural network electrical activity patterns and preventing neurological diseases. From the perspective of biophysics, the activation of magnetic field coupling is the result of the continuous release and propagation of intracellular and extracellular ions, which is very similar to the activation of chemical synaptic coupling through the continuous release of neurotransmitters. In this article, an induction coil is used to connect two HR neurons to stimulate the effect of magnetic field coupling. It is inevitable that time delays can affect the coupling process in the transmission of information, and it should be considered in the coupled model. Firstly, the firing characteristics and bifurcation modes of two coupled HR neurons are studied by using one parameter and two parameters bifurcation. With the increase of propagation delay and coupling gain, the chaotic state of neurons disappears and the high-period window decreases due to the influence of energy transfer between neurons. Then, the synchronization patterns of two HR neurons with different stimulation are analyzed by error diagrams and time series diagrams. It is confirmed that the synchronous pattern has certain regularity and is related not only to the neurons with large stimulation current but also to the time delay and coupling gain. The research conclusions of this article will provide the corresponding theoretical basis for medical experiments.

Energy evolution in function neuronal network under different coupling channel

“…The flow of ions continuous exchange of charges and neurotransmitter just changed the distribution of electric field and/or magnetic field, which is induced by the moving charge and variation of electric field in the media [48]. According to the law of electromagnetic induction, the electric field coupling between neuronal circuits can be achieved through capacitor connections [49,50], and the magnetic field coupling can be verified through inductor [51][52][53]. A portion of the energy of the coupling circuit is pumped and stored in the coupling channel temporarily.…”