Study On Oscillation Characteristics Of Neural Mass Model With Multi-feedback Loops Using Bifurcation Theory

The study of neural oscillations plays a crucial role in completing various advanced cognitive tasks and is useful for estimating neural electrical activities.Rhythms are an important characterization of neural oscillations.Neural mass models(NMMs)with rich and complex nonlinear dynamics provide an important and parsimonious description of neural oscillation rhythms.From the viewpoint of neuroinformatics perspective,these models provide a valid tool to explore the regulating mechanism of neural oscillation rhythms.Multiple feedback loops and external inputs in NMMs regulate the dynamics of oscillation rhythms.Thus,the mechanisms of neural oscillations rhythms underlined by multi-feedback and multi-input still remain to be explored.This paper aims to understand neural oscillation characteristics by studying oscillation rhythms of neural mass models.Most studies of neural oscillations characteristics are conducted based on Jansen & Rit model which is composed of excitatory and inhibitory feedback loops.However,the real neural mass includes multiple feedback loops.Therefore,the mechanism of neural oscillation rhythms underlined by multi-feedback still remains to be addressed.External inputs play an important role in the regulation of neural oscillations rhythms.Related researches mainly exploited the influence of single input;however,it is still unclear how multi-input exerts an effect on the regulation of oscillation rhythms.The chaos oscillation with irregular rhythms is a special type of neural oscillations;there is little related research to reveal the mechanism of chaotic oscillation rhythms.This research focuses on Ursino's model which is a typical multi-feedback model.There are three feedback loops in this model: excitatory feedback loop,slow inhibitory feedback loop and fast inhibitory feedback loop with a self-feedback loop.In this employed model,there are two external inputs to fast inhibitory feedback loop and pyramidal neurons,respectively.In addition,the period doubling bifurcations with respect to some parameters induce chaotic oscillations.Thus,this model provides a valid testbed to explore the mechanisms of neural oscillations.The bifurcation and spectral characteristics analysis are the main researching methods of this study.1.The effect of fast inhibitory feedback loop on neural oscillations.Codimension one and two bifurcation analyses with respect to the loop are conducted and the parameters regions of various typical dynamics are determined.The frequency curves and frequency distribution diagrams of induced and intrinsic oscillation rhythms are obtained.The results provide insight into how the loop exerts impact on the dynamics of oscillation rhythms.2.Codimension one and two bifurcation analyses with respect to the two inputs are conducted.The bifurcation parameters regions are determined.The frequency curves and the frequency distribution diagram of oscillation rhythms are obtained.The results elucidate the regulating mechanism of oscillation rhythms underlined by the two inputs.3.The period doubling bifurcations with respect to some parameters of the model are conducted.Period doubling bifurcations analysis of these parameters is helpful for deternining the regions of order and chaos in parameters space.The frequency curves of periods are obtained.The results provide insight into how the chaos induced by period doubling bifurcation to influence oscillation rhythms.In conclusion,these results reveal that fast inhibitory feedback loop plays an important role in the generation and regulation of neural oscillation rhythms,especially in the high frequency oscillations.Furthermore,the interaction of the self feedback strength and other model parameters in the fast inhibitory feedback loop exert important effect on neural oscillation rhythms.The input to the fast inhibitory feedback loop is useful for oscillation rhythm regulation.The chaos induced by period doubling bifurcation inhibits neural oscillations.The study can shed light the regulation mechanism of neural oscillation rhythms in the neural mass model,thus helps understand the oscillation mechanism of more complex cognitive tasks.