Stability And Synchronization In Neural Networks With Time-varying Delays

The delayed neural networks exhibiting the abundant dynamical behaviors are a subfield of the delayed systems. Due to their comprehensive applications in pattern recognition, image processing and optimized calculation, the denamical issue of the delayed neural networks have attracted many scholars for research. This paper is concerned with the stability and synchronization for neural networks with time-varying delays. It consists of six chapters.1. Stability analysis for the bidirectional associative memory (BAM) neural network model with time-varying delaysNeither the boundedness and the monotony on these activation functions nor the differentiability on the time-varying delays are assumed. By employing Lyapunov functional and the linear matrix inequality (LMI) approach, several new sufficient conditions in LMI form are obtained to ensure the existence, uniqueness and global exponential stability of equilibrium point for the neural networks. Moreover, the exponential convergence rate index is estimated. The results obtained perfect and generalize the present conclusions.2. The state estimation for neural networks with both discrete and distributed time-varying delaysBy constructing appropriate Lyapunov-Krasovskii functional and employing Newton-Leibniz formulation and linear matrix inequality (LMI) technique, a delay-interval-dependent condition is developed to estimate the neuron state with some available output measurements such that the error-state system is globally asymptotically stable. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of their derivative are removed.3. Synchronization analysis for an array of coupled stochastic discrete-time neural networks with both discrete and distributed time-varying delaysBy utilizing a novel Lyapunov-Krasovskii functional and the Kronecker product, it is shown that the addressed stochastic discrete-time neural networks is synchronized if certain linear matrix inequalities (LMIs) are feasible. Neither any model transformation nor free-weighting matrices are employed in the derivation of the results obtained, thus in comparison with the existing criteria, the results are less conservative.4. Synchronization analysis for an array of hybrid coupled neural networks with discrete time-varying delays, continuously distributed time-varying delays and nonlinear coupling as wellBy utilizing Lyapunov-Krasovskii functional, a special coupling matrix and the Kronecker product, several LMI criteria are developed to achieve cluster, local and complete synchronization for addressed coupled neural networks. Under a uniform scheme, it is easy to achieve different synchronization form for different combination among the number of synchronous group, the number of the state vector in each different group and the coupling matrices.5. Cluster synchronization analysis for discrete-time complex networks with both discrete and distributed time-varying delaysBy utilizing a proper Lyapunov-Krasovskii functional, a special coupling matrix and the Kronecker product, a cluster synchronized criterion is developed for addressed complex networks. It is shown that the addressed discrete-time complex networks is achieved cluster synchronization if certain linear matrix inequality (LMI) is feasible.