{"title":"张神经网络求解时变非线性方程组的收敛性和稳定性结果","authors":"Yunong Zhang, Yanyan Shi, Lin Xiao, Bingguo Mu","doi":"10.1109/ICNC.2012.6234592","DOIUrl":null,"url":null,"abstract":"For solving systems of time-varying nonlinear equations, this paper generalizes a special kind of recurrent neural network by using a design method proposed by Zhang et al. Such a recurrent neural network (termed Zhang neural network, ZNN) is designed based on an indefinite error-function instead of a norm-based energy function. Theoretical analysis and results of convergence and stability are presented to show the desirable properties (e.g., large-scale exponential convergence) of ZNN via two different activation-function arrays for solving systems of time-varying nonlinear equations. Computer-simulation results substantiate further the theoretical analysis and efficacy of ZNN for solving systems of time-varying nonlinear equations.","PeriodicalId":404981,"journal":{"name":"2012 8th International Conference on Natural Computation","volume":"38 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"Convergence and stability results of Zhang neural network solving systems of time-varying nonlinear equations\",\"authors\":\"Yunong Zhang, Yanyan Shi, Lin Xiao, Bingguo Mu\",\"doi\":\"10.1109/ICNC.2012.6234592\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For solving systems of time-varying nonlinear equations, this paper generalizes a special kind of recurrent neural network by using a design method proposed by Zhang et al. Such a recurrent neural network (termed Zhang neural network, ZNN) is designed based on an indefinite error-function instead of a norm-based energy function. Theoretical analysis and results of convergence and stability are presented to show the desirable properties (e.g., large-scale exponential convergence) of ZNN via two different activation-function arrays for solving systems of time-varying nonlinear equations. Computer-simulation results substantiate further the theoretical analysis and efficacy of ZNN for solving systems of time-varying nonlinear equations.\",\"PeriodicalId\":404981,\"journal\":{\"name\":\"2012 8th International Conference on Natural Computation\",\"volume\":\"38 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-05-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2012 8th International Conference on Natural Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICNC.2012.6234592\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2012 8th International Conference on Natural Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICNC.2012.6234592","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Convergence and stability results of Zhang neural network solving systems of time-varying nonlinear equations
For solving systems of time-varying nonlinear equations, this paper generalizes a special kind of recurrent neural network by using a design method proposed by Zhang et al. Such a recurrent neural network (termed Zhang neural network, ZNN) is designed based on an indefinite error-function instead of a norm-based energy function. Theoretical analysis and results of convergence and stability are presented to show the desirable properties (e.g., large-scale exponential convergence) of ZNN via two different activation-function arrays for solving systems of time-varying nonlinear equations. Computer-simulation results substantiate further the theoretical analysis and efficacy of ZNN for solving systems of time-varying nonlinear equations.