The Application Of Marotto Theorem In The Discrete Hindmarsh-Rose Model

In this thesis, a map-based Hindmarsh-Rose model (HR model, for short) is obtained by using Euler discrete format. At first, the existence condition and stability of the fixed points are investigated by taking into account the discrete HR model. Second, a sufficient condition that HR model exists chaos in the sense of Marotto's definition is obtained. And numerical simulation including maximum Lyapunov exponents, bifurcation diagrams are used to identify the theoretical results. Finally, we end our thesis with summary.The layout of this thesis is as follows.In Chapter 1, a brief review is introduced concerning nonlinear dynamical system theory, such as center manifolds theorem, Lyapunov exponents, Hopf bifurcation, chaos, the reduction of nonlinear dynamical system, and four classic neural models.In Chapter 2, the existence condition and stability of fixed point of HR model are investigated by using the qualitative theory and bifurcation theory. A sufficient condition that HR model exists chaos in the sense of Marotto's definition is obtained.In Chaper 3, we briefly conclude the thesis..