Adaptive Synchronization Control Of Mode-dependent Stochastic Neutral-type Neural Networks

As it is well known, the stability and synchronization of neural networks can be applied to create chemical and biological systems, secure communication systems, information science, image processing and so on. The practice of neural network models attracts researchers to investigate the stability and stabilization of the neutral-type neural network. The synchronization for the drive system and the response system is achieved when the states of the error system can eventually approach zero. In recent years, different control methods, like adaptive control, are derived to achieve different concepts of synchronization, such as generalized synchronization, lag synchronization, phase synchronization, etc.Since the fact that some physical systems in the real world can be described by neutral-type models, neutral-type systems which depend on the delays of state and state derivative have attracted a lot of attention. However, the synchronization of coupled neutral-type neural networks has been rarely researched.Random and abrupt variations, such as sudden environmental disturbance, component failures or repairs, changing subsystem interconnections, may change the behaviors of dynamic systems. The mode-dependent neural networks have the ability of describing those variations, by switching (or jumping) among different modes, governed by a Markovian chain. Therefore, the state space of the network contains continuous and discrete states:the dynamics of the network are continuous and the Markovian jumping between different modes is discrete.Furthermore, in real world, the fluctuations from the release of neurotransmitters and other probabilistic causes may affect the stability property of neutral-type neural networks. However, due to the difficulty of mathematics, noise perturbations have been seldom applied to study synchronization problems. Adding noise perturbations to the model makes the results obtained in this pape rmore general and realistic. In practice, the weight coefficients of neurons rely on certain capacitance and resistance values which are subject to parameter uncertainties.Time-delays present complex and unpredictable behaviors in practice and are often caused by the finite switching speeds of the amplifiers. The neural signal propagation is often distributed during a certain time period with the presence of an amount of parallel pathways with a variety of axon sizes and lengths. Hence, the distributed delays would be put in our models.Motivated by above causes, this paper mainly researches the following five parts:1) Based on Lyapunov-Krasovskii stability theory and stochastic analysis approaches, several new criteria are derived to guarantee the robust stability of the neutral-type with both discrete and distributed time-varying delays.2) The global robust exponential stability is investigated for uncertain neural networks of neutral-type with mixed time delays using Lyapunov-Krasovskii stability theory.3) Based on LaShall-type invariance principle for stochastic differential delay equations, the stochastic analysis theory and the adaptive feedback control technique, an adaptive feed back controller is proposed to achieve the synchronization of neutral-type neural networks with stochastic perturbation and parameter uncertainties.4) By the M-matrix approach and the stochastic analysis method, some sufficient conditions are obtained to ensure three kinds of adaptive synchronization for the stochastic neutral-type neural networks with Markovian switching parameters:almost sure asymptotical synchronization, exponential synchronization in pth moment and almost sure exponential synchronization.5) The mode-dependent projective synchronization problem of a couple of stochastic neutral-type neural networks with distributed time-delays is investigated by using the Lyapunov stability theory and the adaptive control method.