The Qualitative Analysis Of Map-based BVP Model

In this thesis, a map-based BVP model is obtained by using Euler formula. At first, the existence condition of the fixed point and its stability are investigated by taking into account the discrete BVP model. Second, according to the qualitative theory and bifurcation analysis, the study shows that the map-based BVP model includes very rich bifurcation phenomena such as saddle-node bifurcation, Neimark-Sacker bifurcation and so on. Finally, a set of sufficient conditions that BVP model exists chaos is obtained in the sense of Marotto's definition.The layout of this thesis is as follows.In Chapter 1, a brief review is introduced concerning dynamical theory, such as the Poincarémap, the theory of bifurcation, chaos of nonlinear dynamical systems and three classical neural models.In Chapter 2, by using the qualitative analysis and bifurcation theory , the condition of the existence of fixed point and its stability of BVP model are investigated. Some specific bifurcations, for example, saddle-node bifurcation, Neimark-Sacker bifurcation, preiod-2 circle, and a set of sufficient conditions in the Marotto's definition of chaos are obtained.In Chapter 3, we briefly conclude the thesis.