Dynamical Mechanisms And Their Applications Of Complex Neural Networks

Study on dynamical behaviors and their application of complex neural networks has long received extensive attention from researchers working in systems and intelligent control areas, because of their successful application in many areas such as pattern recog-nition, image processing, optimization problem and secure communication. Therefore, study on the dynamical behaviors and their application is of profound theoretical and practical significance, and may further enhance the possibility of applying control theory of complex neural networks to engineering areas.This thesis, based on Lyapunov functional theory, free-weighting matrix, Green for-mula, Leibniz-Newton formula, M-matrix theory, impulsive control, coupling method, Holder inequality, systematically and deeply investigates dynamical behaviors of com-plex neural networks, and thoroughly elaborates theoretical analysis and application research. Especially, synchronization of delayed neural network models with reaction-diffusion terms, impulsive stabilization of delayed T-S fuzzy neural network systems, expo-nential dissipativity of delayed Cohen-Grossberg neural networks with reaction-diffusion terms are deeply analyzed, and some significant results have been obtained.The main contributions of this thesis are listed as follows:1. The existence and global asymptotic stability of equilibriums of delayed recur-rent neural networks and competitive neural network systems with distributed delays are studied, respectively. Under different constrains on activation functions, sufficient criteria for stability of delayed neural networks are derived, respectively.2. The global robust asymptotic stability of periodic solutions of delayed recurrent switched neural networks with parameter uncertainties and existence and exponential stability of periodic solutions of delayed Cohen-Grossberg neural networks with reaction-diffusion terms are discussed, and the proposed criteria are strictly proved. Especially, when analyzing the periodicity of delayed recurrent switched neural networks with param-eter uncertainties, some rigorous assumptions (such as bounded derivative of time-varying delay, boundedness and monotonousness of activation functions) are removed, which leads to less conservative results.3. On the basis of coupled method and drive-response synchronization principle, pa-rameter identification and coupled synchronization of a class of delayed neural networks, synchronization of delayed neural networks with reaction-diffusion terms are analyzed, respectively. Some sufficient criteria for synchronization of system states are constructed and numerical simulations are also provided. In particular, chaotic synchronization char-acteristic is firstly attempted to apply to delayed neural networks with reaction-diffusion terms.4. For a class of reaction-diffusion Cohen-Grossberg neural networks with both dis-crete and distributed delays, their exponential dissipativities are analyzed. By combining diffusion operator and M-matrix property and employing Holder inequality, several cri-teria are proposed for the exponential dissipativity and spatial locations of invariant sets and attractive sets are indicated under dropping off the boundedness, monotonicity and differentiability of activation functions and boudedness of average delay (?) sK_ij(s)ds.5. Based on T-S fuzzy modeling concept, a class of delayed T-S fuzzy neural net-work systems are constructed and the impulsive stabilization design is developed. The ideas of fixed and variable impulsive interval control are merged into the resolution of the problem, which ensures high flexibility of the presented design method. Meanwhile, adaptive stabilization problem of delayed neural networks with reaction-diffusion terms is also addressed. Via translation transformation of states, the global asymptotic stability problem of system solutions is equivalent to how to design a controller making the trivial solution of transformed system be globally asymptotically stable.6. The effectiveness and importance of theoretical results for dynamical mechanisms of delayed neural networks is illustrated by combining with some real-world examples, for instance, quadratic programming problem, secure communication of signals and non-linear system identification. It is worth noting that little study has been performed on applications of stability criteria of neural networks with reaction-diffusion terms in plant cell percolation models and water quality transmigration equations of river pollutants.Finally, some conclusions of the thesis and prospects to be further studied are pre-sented.