Effects Of External Stimuli On Mixed Bursting And Their Dynamical Analysis

Breathing movement is a kind of unconscious and complex behavior,which is controlled by neurons in brain stem.Breathing movement consists two stages,inspiration(absorbing oxygen)and expiration(releasing carbon dioxide).Respiratory rhythm is generated,monitored and regulated by neurons located in the main brain stems,pons and medulla.Pre-B(?)tzinger complex(referred to as PBC),which located in the lateral area of mammalian medulla,is responsible for the respiratory rhythm.When neurons are stimulated externally,their firing patterns will be changed correspondingly.Therefore,it is of great significance to study the influence of external excitation on respiratory rhythm and their transition mechanism.Square wave current and triangular wave current are simple and easy to be realized.By regulating three variables of square wave current and triangular wave current,we investigate the effects of square wave current and triangular wave current on neuronal firing patterns.This paper consists of four parts.Firstly,we give the introduction,which mainly includes background of the biological and dynamical research.In Second part,the effects of square wave current on the mixed bursting of pre-B(?)tzinger complex neurons are investigate by regulating three variables of square current.By one-and two-parameter bifurcation analysis,the dynamic mechanism of generation and transition of mixed bursting are explored.In Third part,the influence of triangular wave current as external excitation on the mixed bursting are studied.The difference dynamical effects on the mixed bursting of neuron are compared between square wave current and triangular wave current.The conclusions and prospects are given in last part.The results show that both square wave current and triangular wave current can induce neurons to produce different types of mixed bursting,and their generation are directly related to the currents.The three variables of current,such as current intensity max,period p and duty dc have different effects on the mixed bursting.It is found that the current intensity has a great influence on the amplitude of firing within the bursting.The current period directly determines the period,the duration and the shape of the mixed bursting.Both the square wave current and triangular wave current have the similar effects on the mixed bursting.At the same time,by the dynamical analysis,it is found that the saddle node bifurcation of equilibrium and homoclinic bifurcation of limit cycle are closely related to the generation of mixed bursting.The results of this paper can provide some reference for further understanding the mechanism of mixed bursting in the neural system.