Stability Analysis Of Delayed Neural Networks On Time Scales

Due to unification of continuous and discrete dynamic properties,dynamic equations on time scales have aroused wide concern of scholars.The study of dynamics equation on time scales reveals the dynamic equation under the condition of discrete and continuous shown by the nature of the similarities and differences,and is more general.Therefore,to analyze problems by employment of relative theory on time scales could provide new idea and useful tools for the research of neural network.This thesis principally analyze stability of neural networks with time delays on time scales.The main contents of this thesis are threefold.(1)Invariant set and periodicity for delayed neural networks on time scales are discussed.Based calculus on time scales,we apply Lyapunov functional method and inequality technique to construct invariant set and obtain the existence of a globally exponential periodic solution in the invariant set.(2)Scale-type stability for neural networks with unbounded time-varying delays is studied.By utilizing calculus on time scales,inequality technique and linear matrix inequality tool,new sufficient conditions for the global exponential stability and global asymptotic stability of such neural networks on time scales are studied.(3)The exponential stability of periodic solution of neural networks with distributed delays on time scales are studied.Employing contraction mapping theorem and inequalities on time scales,new criterion for the existence and exponential stability of periodic solution of such networks on time scales are derived.Numerical simulations are given to illustrate the effectiveness of our new results.