Stability Analysis Of A Ring Neural Network System

In this paper,the delay-dependent and delay-independent stability of a ring neural network system is studied.Firstly,the influence of self-feedback term on the stability of neural network system is discussed.Secondly,the stability of four-neuron bidirectional annular multi-time delay neural network system is analyzed.In the first chapter,the historical background,significance and research status of time-delay annular neural network system are described,and the neural network model of this paper is introduced.In the second chapter,the stability of a time-delay ring neural network system with self-feedback and small-world connection is studied.Firstly,the delay-dependent stability is analyzed by using the Lyapunov functional method,and the global stability interval of time delay is established.Secondly,the delay-independent stability is studied according to the Schur-Cohn criterion,and the relationship between the self-feedback weight and the system stability is established.Finally,the conclusion is proved by numerical simulation.In chapter 3,the stability of bidirectional annular neural network system with double time delays is analyzed.Firstly,the characteristic equation of the system is decomposed into four first-order factors,and the condition that the zero of each factor is negative real part is discussed by constructing auxiliary functions.Moreover,the delay-independent and delay-dependent stability conclusions are established.Secondly,the stability of the linear neural network system is discussed when the connection between two adjacent neurons is cut off.The numerical simulation results show that the linear neural network system has a wider range of the parameters,that is,it is more easier to be stabilized than the ring architecture.In chapter 4,for a class of second-order ODE systems and infinite dimensional coupled systems with ODE-wave equations formed by boundary connections,the problem is firstly transformed into an abstract development equation,and then the problem of its wellness and stability is studied by using the0 C semigroup method.Secondly,the asymptotic expressions of eigenvalues and eigenvectors of system operators are analyzed.