Dynamic Analysis Of A Two-compartment Pre-B(?)tzinnger Complex Model And Approximation System

The pre-B(?)tzinger complex(PBC)in the mammalian brain region is the key site for the generation of respiratory rhythm.Therefore,it is very important to study the dynamic of respiratory neurons and neural network models.In this paper,the dynamic characteristics of a class of PBC neuron model and its approx-imation system are studied by using the theory and method of nonlinear dynamics and numerical simulation.The main research work is as follows:First,a two-compartment PBC neuron model was approximate and modified to a single-compartment model,and external stimulus current was applied to the single-compartment neurons.Bifurcation analysis and fast/slow decomposition techniques showed that the stimulus current could drive abundant bursting as per-sistent sodium current and calcium activation current.In addition,the fast and slow analysis and phase plane analysis were combined to explain the dynamic mechanism of the cluster discharge.By controlling the time state constants and the stimulation current,a variety of firing modes were observed,thus providing a solution for optimizing the firing patterns of PBC neurons.Second,the synchronization degree of two-compartment PBC neurons un-der magnetic current stimulation was studied.Firstly,the firing patterns of the two compartments under different[IP3]were discussed,and the effects of differ-ent parameters on firing rhythm were analyzed by InterSpike Intervals(ISI)and correlation coefficient.Then,an important parameter[IP3]in the dendritic com-partment was controlled to reveal the synchronization and transition between the two compartments by adjusting the coupling strength between the somatic com-partment and dendritic compartment.Finally,the dynamic effects of the magnetic flux on the somatic compartment were analyzed from three aspects of the fre-quency,amplitude and deviation of the magnetic flux.The results show that the magnetic flux frequency has a strong robustness to the synchronization and tran-sition,while the system has a continuous dependence on the initial value.Thirdly,the correlation between the degree of synchronization and the type of synchronization is studied for the forced path coupling network.Two PBC neurons were coupled by electrical synapses by applying an elliptical path to the single-compartment approximation system,and a coupling network model was established.Based on the cases with no delay,symmetric delay and asymmetric delay,the relationship between several common synchronization and correlation coefficient is discussed by means of ISI bifurcation,correlation coefficient and maximum synchronization error.The results show that the phase synchroniza-tion of the two coupled neurons is closely related to the weak correlation,that is,phase synchronization and lag synchronization may occur in the case of incom-plete synchronization.By controlling the time delay and coupling strength in the approximate PBC network model,it is not only revealed that PBC is the law of transmission and transition,but also found that there is complex synchronization behavior in the coupled chaotic network.