The Analysis On Synchronization And Stability Of Several Neural Networks And Asymptotic Distribution Of Robust Estimator In Spatial Autoregressive Models

In modern society,with the continuous development of communication networks,the research on neural networks has attracted extensive attention in the fields of engineering and science.However,as a non negligible part of the time-delay system,in the actual implementation process,due to the objective existence of time-delay,it is likely to cause the oscillation behavior,divergence and even instability of the system.In addition,due to the wide application prospect of neural networks in the fields of pattern recognition,signal and image processing,associative memory,automatic control and so on,more and more researchers show great interest in the dynamic behavior of neural networks.Therefore,as an important part of the dynamic behavior of neural networks,the synchronization control and stability analysis of time-delay neural networks have become two hot research topics.In the second to fourth chapters of this paper,we mainly discuss the synchronization control and the stability of equilibrium solutions of several kinds of time-varying delay neural networks.The specific research contents are as follows:In Chapter 2,we are concerned about the global asymptotic synchronisation for a class of fuzzy master-slave inertial neural networks with time-varying delays.At present,most of the research on the global asymptotic synchronisation of fuzzy master-slave inertial neural networks with time-varying delays adopt the matrix measure method,linear matrix inequality approach and integral inequality method.While in our paper,we attain three criteria to assure the global asymptotic synchronisation between the master system and the slave system by designing three classes of different novel controllers via the maximum-value analysis approach.The controllers designed and the maximum-value method used in this paper are completely novel compared with these in the existing literatures,which enrich and extend the published results.In Chapter 3,we focus on the finite-time synchronization for drive-response BAM neural networks with time-varying delays.Instead of using the finite-time stability theorem and integral inequality method,by using the maximum-value method,two new criteria are obtained to ensure the finite-time synchronization for the considered driveresponse systems.The inequalities in our paper,applied to obtaining the maximum-value and designing the novel controllers,are different from those in existing papers.In Chapter 4,the existence-uniqueness and asymptotic stability of equilibrium solutions for a class of quaternion-valued fuzzy BAM neural networks with delays are considered.Firstly,by applying Homeomorphism theorem with contradictory method and novel analytical techniques,a sufficient criterion ensuring the existence-uniqueness of equilibrium solutions of the concerned quaternion-valued fuzzy BAM neural networks is achieved.Then,without utilizing V’(t)<0,by using integral inequality approach,a condition assuring the global asymptotic stability of equilibrium solutions for above neural networks is achieved.Utilizing contradictory method studying the existence-uniqueness of equilibrium solutions and utilizing integral inequality approach studying the asymptotic stability for neural networks are new research approaches.On the other hand,due to the wide existence of outliers in spatial data,these potential outliers will have a significant impact on parameter estimation and corresponding statistical inference.However,outliers themselves are likely to contain some information of the sample itself.Therefore,it is often inappropriate to simply delete the data.Based on these facts,under the framework of maximum likelihood estimation(MLE),we investigate the asymptotic distribution of robust ML estimator under the mixed spatial autoregressive models with outliers and compare it with that of the ML estimator.Furthermore,based on the asymptotic theoretical result,we conduct the confidence interval of robust MLE and MLE.Similar to the results of MLE,we construct the second-ordercorrected robust confidence interval using the parametric and semi-parametric bootstrap method.Simulation studies using Monte Carlo show that the robust estimator with the Huber loss function is more accurate and outperforms the MLE in most sample settings when data is contaminated by outliers.Then the use of the method is demonstrated in the analysis of the Neighborhood Crimes Data and the Boston Housing Price Data.The results further support the eligibility of the robust method in practical situations.