Complex Dynamical Study Of The Effect Of Autaptic On Neural Electrical Activity

Bursting is a complex nonlinear phenomenon of the nervous system,which is diverse due to different fast and slow time scales,and is modulated by the excitatory or inhibitory effects to achieve the physiological functions.Recently,many studies have found the paradoxical phenomena contrary to the common concept that the inhibitory effect induces the electrical activity to decrease or the excitatory effect induces the discharge activity to increase,which enriches the connotation of the nonlinear dynamics.This paper focuses on the paradoxical phenomenon that inhibitory and excitatory autaptic feedback can induce cluster firing and its bifurcation mechanism,targeting two different types of mixed cluster firing,using fast and slow variable separation.The main study of the thesis is divided into two parts:Firstly,the "Circle/Fold Cycle" type of bursting was studied by numerical simulations and the effect of fast autaptic feedback on the electrical activity of the bursting was studied through spike trains and average firing frequencies.It was found that both inhibitory and excitatory self-feedback currents induced paradoxical phenomena in this type of bursting.By using the fast/slow variable dissection method,the complex dynamics of the bursting are acquired,which is that the depolarization block behavior appears after the burst and before the quiescent state.The burst begins from a saddle-node bifurcation in an invariant cycle(SNIC)and terminates at a fold limit cycle(FLC)bifurcation.Furthermore,the FLC bifurcation is identified to play a key role in generating the paradoxical phenomenon.The results show that the appropriate autaptic current does not change the type of bursting,but that inhibitory self-feedback causes a leftward shift of the bifurcation point.The change of bifurcation point leads the parameter range of the burst to widen,the number of spikes per burst to become larger,and the average firing frequency to turn higher.Unlike the inhibitory autapse,the excitatory autapse induces the bifurcation point to shift rightward,thus reducing the bursting activity.Secondly,using the "Sub Hopf/Homoclinic" type of bursting as an object of study,the application of inhibitory autaptic currents caused a decrease in the number of peaks within the burst of this model,which is the same as the conventional concept of inhibitory action suppressing electrical activity,whereas excitatory self-feedback induced a paradoxical phenomenon in bursting.It was also found that both inhibitory and excitatory conductance strength increments were able to widen the time range corresponding to the depolarization block in the burst.Using fast and slow analysis and model simulations,the results indicate that increases the attraction of the stable focus and decreases the repulsion of the unstable focus,with conductance strength enlarged,whether inhibitory or excitatory,thus widening the range of bifurcation parameters corresponding to the depolarization block and contributing to a larger range of time courses.The depolarization block for this class of bursting corresponds to the onset of bursting activities,and thus depolarization block also plays a key role in the autapse modulation of induced anomalies.It was also found that fast autapse causes a subcritical Hopf bifurcation in the fast subsystem,a fold limit cycle bifurcation,and a shift in the bifurcation point of the homoclinic,leading to a narrowing of the parameter range corresponding to the stable limit cycle.The results of this paper are different from those of the paradoxical phenomena induced by the inhibitory autapse instead of excitatory autapse for the other bursting pattern and by the slow autapse,which present a novel example and regulation mechanism of the paradoxical phenomena of the bursting patterns and show the diversity of the paradoxical phenomena,thus helping understand the potential functions of the bursting and self-feedback modulations of the brain neurons.