Hopf Bifurcation Of Delayed Neural Networks And Consensus Of Multi-agent Systems

Firstly,the basic concepts,research background and research significance of complex network,time delay system,bifurcation and multi-agent systems are briefly introduced,and the main contents and innovative work of this paper are summarized.Secondly,the Hopf bifurcation problems of two delayed neural networks are considered,one is BAM neural networks with seven neurons and seven delays,and the other is 2n-neuron neural networks.These two neural network models are the first to be studied,which has a certain significance for enriching and promoting the development of neural networks.In addition,because they contain more neurons and more delays,so they are closer to reality and more conducive to understanding the reality of the neural networks.The main research method is as follows:Taking the partial delays as a bifurcation parameter,by analyzing the characteristic equation of the linearized system,the critical value of the bifurcation of the system and the sufficient condition for making the system produce the bifurcation are obtained.Furthermore,by using the central manifold theorem and the normal form method,the stability and direction of the Hopf bifurcation and the properties of the bifurcation period are analyzed.Then,the consensus problems of a class of second-order linear multi-agent systems are analyzed and studied.In which,each agent has its own speed and position,under the design of the consensus protocol,each agent gradually tends to the same state over time.Later,the two consensus problems of linear and nonlinear multi-agent systems are studied,respectively.For the linear multi-agent systems,under the simplified consensus protocol,the complex information exchange between agents is confined in a directed spanning tree.For the nonlinear multi-agent systems,under the consensus protocol with feedback gain,the operating state of each agent is affected by its own state.Through the derivation calculation,it obtains the conditions which are superior to some papers.Their research methods are:design consensus protocol,by using graph theory and some of the properties of the matrix,the conditions that make the error systems stable at the origin are obtained.Whether the real parts of the eigenvalues of the coefficient matrix of the linear systems are all negative is an important condition to judge whether the systems are stable or not.The main method of judging the stability of nonlinear systems is the Lyapunov second method,that is,by constructing the V function to judge.In the end,the work done in this paper is summarized and the future research directions are described.