Effect Of Ion Channels On Respiratory Rhythm Dynamics In The Pre-B?tzinger Complex

The abnormal respiratory rhythm of respiratory system is an important health issue that has attracted much research attention. An essential goal of studying the dynamical behaviors of the respiratory system is to study and control the abnormal respiratory rhythms based on the understanding of the normal dynamic behaviors of the system.Nonlinearity is a basic characteristic of the nature, and most realistic systems are nonlinear. Life systems are highly nonlinear, and the motion of neuron systems also exhibit nonlinear characteristics. With the development of nonlinear theory, nonlinear methods have widely been applied to various research fields. Therefore, it is natural to study the neuron systems using nonlinear dynamical methods, which will further promote the investigation and treating of relative disease from a nonlinear point of view.The investigation of the mechanism of respiratory rhythm has important practical significance. It helps to understand the basic physiological activities of human being and other animal species, and also facilitates the treatment of certain diseases related to respiratory rhythm.In this thesis, using bifurcation and multi-time scale theories, we investigate the influences of different fast-slow ion channels on the respiratory rhythm. Based on the pre-B?tzinger complex models, we investigate the effects of different fast-slow ion channels on the firing patterns both in the single and coupled neuronal systems, by applying nonlinear dynamical methods. The main results we obtain are as follows:?1? With the low conductance of Na+, we investigate the effects of conductance K+ on the firing patterns. According to the fast-slow dynamical analysis, we find that with the increasing of conductance K+,the system transits from "subhopf / subhopf" bursting and "subhopf /homoclinic" bursting to "fold /homoclinic" bursting; With the high conductance of Na+, the system transits from "subHopf/subHopf" bursting and "fold cycle/homoclinic" bursting to "fold/homoclinic" bursting. And the transits point from supercritical Hopf bifurcation to subcritical Hopf bifurcation is highly related to the conductance Na+.?2? For the soma-dendrite pre-B?tzinger complex model, we study the influence of IP₃ on the firing rhythms of the pre-B?tzinger complex. We found that with the high concentration of IP₃, the firing pattern is very different from the case of lower influence of IP₃ . And the periodic oscillation for in-phase and anti-phase is quiet difference.?3? In the pre-B?tzinger complex model, with two parameters VSERCA and IP₃ changed, we found that the oscillation Ca2+ is periodic and highly depending on VSERCA and IP₃.