Dynamics Of High-dimensional Neural Networks With Annular Structures

Dynamic behavior is the representation of dynamic system,such as oscillation,chaos and bifurcation.The bifurcation is a significant indicator of the dynamic behavior of the dynamic system.By analyzing the characteristics of the bifurcation,one can seize some important intrinsic properties of the dynamic system.This will help people understand some of the factors that affect the critical features of the system,so that information on system stability and other features can be captured and used.Currently,bifurcation theory has become the mathematical basis of research and application in life sciences,artificial intelligence and other domains.It is of great significance to the improvement of nonlinear discipline and the promotion of engineering practice.A large number of experiments show that the inevitability of time delay,the possibility of multiple factors,the accuracy of network description and the reliability of network optimization strategy are considered.All these orientations are important for investigating the dynamic behaviour of complex networks.However,current research on the dynamic behaviour of complex networks still has a number of limitations.There are few researches in some aspects,such as the lack of general analysis of high-dimensional networks and the introduction of the concept of fractional order to better describe the network model.Therefore,on the basis of the complex network in the real environment,the research of the high-dimension network dynamics merits attention.This paper is interested in the dynamics of complex networks.Based on the theoretical results of predecessors and bifurcation theory,for high-dimension neural networks in integer order(fractional order)and delayed PD-controlled BM neural networks.In-depth exploration of its dynamic bifurcation behavior.The specific work is as follows:(1)Given the design of structural systems.The dynamic behavior of an integer neural network on a large scale with a three-ring(hypercyclic)structure is investigated.Using discrete time delay as the bifurcation parameter.The local stability and Hopf bifurcation of such a high-dimensional neural network are analyzed.Research has shown that the network structure(like the number of rings,the number of neurons,the distribution of neurons,etc.)is closely connected to the position of bifurcation(stability threshold)of the neuronal network.(2)Considering the modeling under the concept of fractional order.The dynamic analysis and design problems of a class of time-delay neural networks,which incorporate multiple types of structures based on the fractional order concept are investigated.Usage of the time-delay term in the model as a bifurcation parameter.The sufficient conditions of the Hopf bifurcation phenomenon are inferred,and the influence of fractional order on the grid stability region is revealed.Studies have shown that the smaller the fractional order,the greater the delay in Hopf bifurcation.By selecting the appropriate fractionation order and system parameters,the network stability threshold at the equilibrium point can be effectively monitored.(3)Given the modelling under the control strategy,the stability of the BM neural network and the Hopf bifurcation issue under the new PD delay controller are investigated.Using the controller as the search point,the critical points of bifurcation of controlled and uncontrolled networks are compared.The research shows that the adjustment of control parameters can be used as an effective means of achieving the dynamic behavior of the network.Based on the research of this paper,it is found that the time delay,feedback parameters,fractional order,structure and dimension of the controller are the key factors to determine the dynamic behavior of the network.Evidently,by using these terms of influence,the advance or delay of the Hopf bifurcation can be controlled,and the ideal bifurcation point can be achieved efficiently.Moreover,depending on the research results obtained in this article,on the one hand it can fill the dynamic theory of nonlinear science.On the other hand,it may provide a theoretical basis for the system and control within the engineering application.