Research On The Stability, Dissipation And Synchronization Of Several Types Of Proportional Delay Neural Networks

Neural networks are nonlinear models for processing information and data,and they have vast potential applications in intelligent robots,image processing,parallel computing,finance,optimization and so forth.The realization of these applications often requires that neural networks have a set of dynamic properties.In the process of information processing,the amplifier has limited switching speed,so the time delay becomes one of the factors to be considered in neural networks,and it often causes networks turbulence,instability,divergence and other undesirable phenomena.The proportional delay is an important type of unbounded delay,and the advantage of proportional delayed neural networks is that we can control running time of the system according to the time delay range permitted by the network.Therefore,it is of great theoretical significance to study the dynamics of proportional delayed neural networks.In this paper,the global stability,dissipativity and synchronization of several types of proportional delayed neural networks are studied.In the first chapter,the development history of neural networks is introduced,and the research status of the stability,dissipativity and synchronization of neural networks with time delays are discussed,respectively.In Chapter 2,the global stability of a class of proportional delayed recurrent neural networks is considered.With the help of the diagonal(semi)stability matrix,appropriate Lyapunov functionals and the delay differential inequality,three sufficient conditions to ensure the global asymptotic stability,global exponential stability and the stability for the equilibrium point of the system are obtained.In Chapter 3,we mainly investigate the polynomial dissipativity for a class of proportional delayed bidirectional associative memory(BAM)neural networks,and the global asymptotic dissi-pativity and global exponential dissipativity for the system are also considered.By constructing more ideal Lyapunov functionals and combining a Halanay inequality,we obtain a set of delay-dependent and delay-independent dissipative conditions,and a set of positive invariant sets and global attractive sets of the system are obtained accordingly.In Chapter 4,we discuss the global polynomial synchronization and global exponential syn-chronization for a class proportional delayed cellular neural networks.Under the help of some more ideal Lyapunov functionals,we obtain a set of sufficient bases to guarantee the relevant syn-chronization of the assumed drive-response system without assuming monotone bounded activation functions.The criteria of this paper are new.In each chapter,the correctness and feasibility of theoretical criteria are verified by detailed numerical examples and computer simulations.These analytical re-sults can lay the foundation for the specific application of the proportional delayed neural networks.