Synchronization Behaviors Of N Identical Rulkov Neurons Under The Star-like And Global Coupling Structures

In the thesis, the cooperative behaviors of map-based neurons cou-pled by electrical and chemical synapses are discussed. According to theory of bifur-cation and chaos of nonlinear dynamical system, and the master stability function method, systems consisting of N identical Rulkov neurons connected by the star-like and the global coupling structures are analyzed, respectively. The stabilities of syn-chronization behaviors and the emergent properties of these systems are concerned.The layout of this thesis is as follows.In Chapter 1, we introduce a brief review concerning background knowledge, such as the structures and types of neurons, the classical mathematical models of neurons, and the synchronizations of coupling neuron networks.In Chapter 2, on the basis of the mathematical mechanism for bursting of single Rulkov map-based neuron model, the theory of bifurcation and chaos of nonlinear dynamical system and master stability function method are applied to take into account the stabilities of synchronized manifolds. The coupling matrixes and their eigenvalues of N identical Rulkov neurons connected by the star-like and global coupling structures are derived. The goal is to explain the relationship between emergence regions and eigenvalues of coupling matrixes, as well as stabilities of syn-chronization behaviors. Numerical simulations are made on the basis of theoretical analysis to identify in-phase and antiphase synchronizations of N identical Rulkov neuron networks under the star-like and global coupling structures, respectively.In Chapter 3, we briefly conclude the thesis.