Optimal Synchronization Control Of Neuronal Network Based On Phase Response

Synchronized oscillating neural activity has been shown to be critical in theadvanced functions of the brain, such as information processing, cognitive, emotionand memory. The abnormal synchronization of neurons in certain regions of the brainis one of the reasons for neurological diseases, such as, a too strong neuronalsynchronization in the thalamus and basal ganglia regions of the brain lead toParkinson’s disease, and the synchronization of neurons in the hippocampus regions isassociates with the epilepsy. Deep brain stimulation technique can cure this disease bymitigating the synchronization of neurons through electrical stimulation. However, atpresent the open-loop deep brain stimulation still has some drawbacks, so, it isimportant for curing these diseases to study the synchronization and its control ofneurons.Based on the transcritical hybrid model which is used to model the basal gangliamotor loop and the Morris-Lecar model, we get the synchronization propensity ofneuronal networks based on the phase response of a single neuron, as well as therelationship between the intrinsic properties of neurons and the synchronization ofnetworks. Then, based on the reduced phase model, the phase resetting control for asingle neuron’s spiking timing regulation and the optimal desynchronizing control forneuronal networks are presented. This paper provides guidance for the neural diseasetreatment. We organize our paper as follows:Firstly, based on the effects of parameters on the phase response of the singleneuron and the synchronization propensity of neuronal networks, the synchronizationproperties based on phase response is presented. Research shows that the neuronswith both phase advancement and delay when exposed to external stimulation cansynchronize better, while neurons with only phase advancement have poor propensityfor synchronization; then the effects of chemical synaptic coupling on the phaseresponse of neurons are investigated, and results show that the effects of coupling onphase response are depending on the coupling type and phase difference. At last, werecognize the dynamic process for neurons from initially coupled to synchronization.Secondly, the burst phase response of the single neuron is investigated, andresults show that the burst phase response displays considerable sensitivity closelyassociated with spike times in the perturbed burster, which can be demonstrated on the mathematical view point; we also built the relationship between the burst phaseresponse and the phase synchronization of bursting neurons.At the end, based on the phase response and synchronization of neurons, wepresent the phase resetting control to change spiking timing of neurons, and theoptimal energy desynchronizing control of discrete determinant system with dynamicprogramming, as well as the optimal energy desynchronizing control of continuousstochastic system by Q-learning combined with artificial neural network. Thesimulation results show the control method is effective.This paper built the relationship between the intrinsic properties of neurons andsynchronization propensity of neural networks, which can help us to understand thepotential mechanism for abnormal firing of neurons. The synchronization control ofneurons can provide guidance for improving the deep brain stimulation treatment..