Research On Global Attracting Sets And Boundedness Of Non-autonomous Complex-valued Neural Networks With Time-varying Delays

Because of having distributed parallel computational features, neural networks have been widely used in intelligent robots, cloud computing, life sciences and other fields, which plays a vital role in the history of modern scientific progress. The dynamical behavior analysis is the theoretical basis, and have attracted the interest of a great number of researchers. In contrast to the previous research results, we have found that due to the complex-valued neural networks(CVNNs) can directly handle complex information, the operational speed and efficiency comparison of real-valued neural networks(RVNNs) have increased significantly, especially in the field of signal processing. At present, many research results are based on Lyapunov stability theory and fixed point theorem, to discuss the stability of nonlinear systems, although classic but old and complex. In this paper, the boundedness and global attractive sets have been discussed, by using the integral inequalities with time delays.Global attracting set is one of the important property in dynamical systems, neural networks having attracting sets mean the networks may have more than one global attractor. However, the premise having global attracting sets are the evolution track of neural networks is uniformly bounded. For the non-autonomous dynamical systems with time delays, the previous local inhibition method and linear matrix inequality which are applied to discuss the global attracting sets is no longer suitable, and using integral inequality is suitable to solve this problem. The integral inequality is often used to investigate the boundedness and global attraction of differential equations, because the form of the solution's estimation of the differential equations is a integral inequality.However, it's necessary to improve the existing integral inequalities for nonlinear system with time delays.This paper mainly obtains the following three works:(1) combined with the existing integral inequality in differential and integral equations, two class of integral inequalities with time delays are drived: one is only single state variable; another has two state variables and it is coupled with the delay integral inequalities. And some sufficient conditions to guarantee the boundedness of the integral inequality are given out.(2) the first class of integral inequality with time delays and relevant theorems are generalized to the non-autonomous Hopfield neural networks with time delays, and several conditions to ascertain uniformly boundedness of the neural networks are derived through quasi-invariant sets. The framework of the global attracting sets is also given. In addition, the integral inequality is further extended and is applied to the neural networks of neutral-type with time delays, similar conclusions are also obtained.(3) some sufficient conditions to guarantee the boundedness of the nonautonomous and complex-valued neural networks with time-varying delays are derived,by studying the second class of integral inequality with time delays and applying the properties of spectral radius of nonnegative matrix. Meanwhile, the estimation of the global attracting sets of neural networks is also given out. Finally, characteristics about asymptotically stability of zero solution of neural networks are also obtained.