Research On Mixed Bursting Pattern And Its Dynamics In Complex Nonlinear System

Respiratory movement is the basis of the entire breathing process and it is a rhythmic activity of the respiratory muscles.The pre-B?tzinger complex is an important part of the generation of the respiratory rhythm.Different external excitations have different effects on the breathing rhythm,and even make the system produce pathological breathing rhythms.Therefore,it is very useful to understand the rhythm pattern and its transition mechanism under the control of parametric excitation and regulation.Based on the improved single-compartment pre-B?tzinger complex excitatory neuron model,we study the influence of external stimulus current and magnetic flux on the complex firing pattern of the respiratory system from the perspective of dynamics.The content of this article consists of four parts.In the first part,we introduce the related biological background and the basic knowledge of nonlinear dynamics;In the second part,we explore how the external stimulus current and magnetic flux affect the firing pattern of the neuron system.Using phase plane analysis,fast-slow analysis and two-parameter bifurcation analysis,we investigate the dynamic mechanism of the conversion between low potential resting and high potential resting state of the bursting.In the third part,the influence of external stimulation current and magnetic flux on the firing pattern of mixed bursting is explored.Non-dimensional analysis of the system is carried out to illustrate the timescale of each variable and dimensionless analysis can eliminate the influence of steel.Use the dimensionless data set,we perform fast-slow analysis and bifurcation analysis to clarify the transition mechanism between mixed bursting patterns.At the same time,we reveal the transition mechanism of the square wave bursting to mixed bursting,and then to amplitude modulation spiking caused by electromagnetic effects.In the fourth part,we give the conclusion and prospect.The results in this paper show that both external stimulation current and magnetic current can significantly affect the firing pattern of the respiratory system.The dynamic mechanism of the transition between low-potential resting and high-potential resting state of bursting is due to the change of bistable structure.The intensity of electromagnetic current can affect the number of somatic bursting of mixed bursting.The generation of mixed bursting is related to the fold and homoclinic bifurcation.External stimulation can make the neuron system produce some complex rhythm pattern particularly similar to the pathological breathing rhythm.We show that bifurcation may be one of the generation mechanisms of these rhythm.The investigation of electric current and magnetic flux acting on the firing patterns of neurons in the pre-B?tzinger complex maybe provide some theoretical basis for understanding the dynamic mechanism of pathological respiratory rhythms.