Existence And Stability Of Solutions For Two Class Neural Networks With Neutral-type And D Operator

In the past decades,due to neural network has been widely used in many fields,at present,many authors have studied many aspects of neural network equation,for example,the existence of solutions of neural network equations,stability,convergence,and so on.In the existing research production,we find that very little people pay attention to the existence and stability of solutions for neural network equations with neural type and D operator.Thus,it is a great significance to study the existence and stability of solutions for neural networks with neutral-type and D operator.We mainly studied the existence and stability of two classes of neural network equations,where,in the second chapter,we considered the existence and global exponential stability of ω periodic solution of the next neural network equations with neutral-type and D operator which satisfies the following initial condition:xi(s)=φ(s),s∈(-∞,0],φi∈BC(R,R),i∈J.In the third chapter,we considered the existence and global stability of anti-periodic solutions for type delayed of high-order Hopfield neural networks with impulses and D operatorThese two kinds of equations are both neural network equations with neutral-type and D operator.By using methods of contraction mapping fixed point theorem,Lyapunov function and differential inequality techniques,several sufficient conditions for the solution and stability of the two equations are obtained,respectively through strict proof,and some applications are presented for the established results.