Stability Analysis For Several Classes Of Neural Networks With Time Delays

Delayed neural networks exhibiting rich dynamical behaviors are a class of complexlarge scale nonlinear dynamical system. Its theoretical research has received considerableattention, especially the stability. Its existence is frequently a source of instability and poorperformance. The stability of delayed neural networks has been extensively studiedbecause of their applications in many areas such as pattern recognition, associativememory, and combinatorial optimization and so on. The paper from the fuzzy rules,random disturbance, mixed delays, inverse Lipschitz function and periodic solution of thetime scale of several classes of neural networks with delays was studied on the stability.Main work is as follows:Firstly, global asymptotic stability of a class of uncertain neural network with twodelays is studied. By constructing a suitable Lyapunov function, using the linear matrixinequality theory, T-S fuzzy model be expanded to uncertain fuzzy neural network withtwo delays, and gives the sufficient conditions of the stability of the system. Through thesimulation example shows the effectiveness of the conclusions.Secondly, The problem of robust asymptotic stability of stochastic Hopfield neuralnetworks with discrete and multiple distributed time-varying delays and inverse Lipschitzactivation function of stochastic Hopfield neural network are investigated.(1) Assumingactivation function is neither differentiability nor strict monotonicity. UsingLyapunov-Krasovskii stable theory, stochastic analysis approaches and LMI controltoolbox in Matlab, the delayed-dependent criteria are derived to ensure robust stability ofthe addressed system. A numerical example is given to demonstrate the effectiveness ofour results.(2) The neural network model satisfies the inverse Lipschitz function condition.Consider stochastic perturbation, using topological degree method and the method ofcontradiction, we get the existence and uniqueness of the equilibrium point of thestochastic Hopfield neural network.Thirdly, the stability of a class of anti-periodic solutions for interval generalbidirectional associative memory (BAM) neural networks with impulses on time scales is analyzed. By using method of coincidence degree and M-matrix theory, we get the uniqueexistence of periodic solution and global sufficient conditions of exponential stability. Atthe same time, through the example shows the effectiveness of the conclusion.