Stability Analysis Of Neutral Neural Networks With Time Dela

Neutral neural networks have been widely used in population ecology,propagation and diffusion models and have attracted much attention.However,in practical applications,due to the signal transmission between neurons and the limited switching speed of hardware equipment,time delays are inevitable.These delays may lead to the oscillation,divergence and chaos of the neural network system,thus affecting the operation of the system.Therefore,the research on the stability of the neural networks with time delays is particularly important.In this paper,the stability of three kinds of neutral neural networks with time delays are studied.Firstly,the stability of neutral neural networks with multiple time-varying delays is considered.The existence and uniqueness of the equilibrium point is proved by using the homeomorphic mapping theory.By constructing the appropriate Lyapunov-Krasovskii functional and using Young inequality,the global asymptotic robust stability criterion of the equilibrium point is obtained.Secondly,the stability of neutral neural networks with S-distributed delays is studied.Generally speaking,discrete delay and distributed delay do not include each other,but Sdistributed delay includes both.After proving the existence and uniqueness of the equilibrium point,by constructing a new Lyapunov-Krasovskii functional and combining the properties of the matrix norm,the global asymptotic stability criterion of the equilibrium point is obtained by using the inequality method.Finally,the stability of stochastic neutral neural networks with S-distributed delays is studied.Using Lyapunov method,semi-martingale convergence theorem and It(?) theorem,the almost sure exponential stability criterion of equilibrium point is obtained.