Firing Patterns And Bifurcation Analysis Of Neurons

Endocrine neurons control the secretion of various hormones in the body,and play a crucial role in the regulation of individual growth,development and somatic function.The electrical activity of neurons contains a large amount of neural information.Therefore,the study on the firing rhythm of neurons is more helpful to understand the encoding and expression of neural information.Based on the three-dimensional endocrine model and combined with the bifurcation theory of dynamical system,this study explore the inherent dynamical properties of the model,as well as the bifurcation and firing patterns of neurons under electromagnetic induction through numerical simulation and theoretical analysis.In the third chapter,the firing patterns of endocrine neurons under the change of calcium ion current are studied.Then,the generation mechanism of the four kind of bursting modes is analyzed by using the fast-slow dynamics method and bifurcation analysis.Finally,the codimensional-2 bifurcation analysis is used to explain the mechanism of transition dynamics between the four kind of bursting modes.The key to mechanism of transition between the bursting patterns depends on the location of the saddle-node bifurcation point,Hopf bifurcation point and limit cycle of the upper branch of Z-shape curve.In chapter 4,the dynamical behaviors of neurons under electromagnetic induction is studied.Firstly,the original model is elevated to four dimensions by introducing magnetic flux variables and induced current.Then,the codimension-one bifurcation and Interspike Intervals analysis are applied to study the bifurcation structure with respect to external stimuli and parameter k0,and two dynamical behaviors are found:period-adding and period-doubling bifurcation leading to chaos.Besides,Hopf bifurcation is specially discussed corresponding to the transformation of the state.Finally,the codimension-two bifurcation analysis shows more details of bifurcation.At the same time,the BogdanovTakens bifurcation point is also analyzed and three bifurcation curves are derived:saddlenode bifurcation curve,Hopf bifurcation curve and homoclinic bifurcation curve.In chapter 5,the firing rhythm of neurons under electromagnetic induction is studied.The firing patterns of endocrine neurons under different coupling strengths are studied according to the different of coupling strengths between magnetic flux variables and membrane potential.Under the weak coupling strength,four kinds of bursting modes are obtained by fast-slow dynamics analysis.Under the strong coupling strength,it is found that different induced currents can produce regular spike,regular bursting,mixed bursting and pseudo-plateau bursting.When the induced current and the external stimulus current act together,there is a great difference in the firing rhythm caused by the change of the stimulus current under different strength induced current.For example,the change of stimulus current causes the endocrine neurons to produce plateau-bursting patterns and mixed bursting under the action of weak induced current.While the induced current is strong,the change of stimulus current causes the endocrine neurons to produce regular mixed mode oscillation and random mixed mode oscillation.