Research On Complete Synchronization Of Neuron Networks And Critical Bifurcation Mechanism Of Hunting Motion Of High-speed Wheelset

In this thesis,the complete synchronization of networks coupled by identical and non-identical nodes is discussed based on chaotic Rulkov neuron network model,in which the excitatory and the inhibitory neurons interact each other through the excita-tory and the inhibitory chemical coupling,respectively.Moreover,bifurcation mecha-nism of wheelset in critical instability state is explored based on high-speed wheelset model.We mainly consider the following three contents:Firstly,for the network coupled with N(N? 2)the excitatory and the inhibitory Rulkov neurons,we have discussed the existence conditions of the synchronization manifold of fixed points.Secondly,if the network is coupled with identical nodes,the master stability equation(MSE)of the arbitrarily connected network is taken into account to determine the synchronization.If the network is coupled with non-identical nodes or with non-dissipative outer coupling matrix,we calculate the stability of the transversal system to determine the synchro-nization of original system.Thirdly,the critical bifurcation mechanisms of hunting motion for the linear wheelset model and the wheelset model with nonlinear equivalent conicity function and nonlinear wheel-rail contact force are discussed,respectively.The mainly content of this thesis is summarized as follows:In chapter 1,we mainly introduce the research background,research status of com-plete synchronization of neuron network and hunting motion of railway trains.Chapter 2 introduces the structure and mathematical models of neurons and neuron networks,and the structure,basic motion,mechanical models of wheelset in wheel-rail system-s.And some conceptions,theorems in dynamical systems are listed and the relations among them are briefly analyzed.In chapter 3,the dynamical behaviors of single chaotic Rulkov neuron model is briefly summarized,and then the Rulkov neuron network coupled by the excitatory and the inhibitory chemical synapses is taken into account.The heterogeneity of nodes and the multiformity of couplings in the network determine the complexity of synchroniza-tion problem.Finally,the existence conditions of the synchronization manifold of fixed points and their proofs are given.For the network coupled with N(N? 2)identical or non-identical Rulkov neurons,the existence of the synchronization manifold of fixed points is related to the control parameters,topology structures,and coupling strength,etc.In chapter 4,the complete synchronization conditions of N(N? 2)identical Rulkov neurons are studied by using the master stability function(MSF)method.The mathematical model of the network is expressed as matrix form.The actual meanings of each part of matrices of the linearized system are explained,and then the master sta-bility equation is given.In addition,through numerical simulation,several topologies satisfying the conditions of synchronization manifold of fixed points are given when three identical Rulkov neurons are considered,and the synchronous regions related to control parameters,coupling strength and synaptic threshold are obtained.In chapter 5,transversal variables are defined and transversal system is obtained if N(N? 2)Rulkov neurons are non-identical or the outer coupling matrix is not a dissipative matrix in the network.The complete synchronization regions of two non-identical Rulkov neurons are obtained by numerical simulation.The effects of the ex-citatory and the inhibitory coupling strength on synchronization of the network are in-vestigated.The waveforms have verified the correctness of these results.In chapter 6,firstly,the effects of the longitudinal/lateral stiffness and the equiva-lent conicity of wheelset tread on the critical speed of wheelset are given in a linear train wheelset model.Secondly,the measured equivalent conicity data of high-speed trains are fitted by a nonlinear function,and wheel-rail contact force function related to lateral displacement is also introduced.Finally,the critical instability mechanism of wheelset is analyzed by supercritical and subcritical Hopf bifurcations,generalized Hopf bifur-cation,fold bifurcation of cycles and Cusp bifurcation of cycles on the parameter plane of longitudinal/lateral stiffness and speed.Chapter 7 summarizes the methods and the conclusions of this thesis.