{"title":"Lorenz系统的自适应功能投影滞后同步","authors":"Tae H. Lee, J. H. Park, S. M. Lee, H. Jung","doi":"10.1999/1307-6892/6425","DOIUrl":null,"url":null,"abstract":"This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion is given for asymptotical stability of the null solution of an error dynamics. Finally, some numerical examples are provided to show the effectiveness of our results. Keywords—Adaptive function projective synchronization, Chaotic system, Lag synchronization, Lyapunov method","PeriodicalId":23764,"journal":{"name":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","volume":"47 1","pages":"1112-1114"},"PeriodicalIF":0.0000,"publicationDate":"2009-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Adaptive Functional Projective Lag Synchronization of Lorenz System\",\"authors\":\"Tae H. Lee, J. H. Park, S. M. Lee, H. Jung\",\"doi\":\"10.1999/1307-6892/6425\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion is given for asymptotical stability of the null solution of an error dynamics. Finally, some numerical examples are provided to show the effectiveness of our results. Keywords—Adaptive function projective synchronization, Chaotic system, Lag synchronization, Lyapunov method\",\"PeriodicalId\":23764,\"journal\":{\"name\":\"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering\",\"volume\":\"47 1\",\"pages\":\"1112-1114\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-12-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1999/1307-6892/6425\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1999/1307-6892/6425","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Adaptive Functional Projective Lag Synchronization of Lorenz System
This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion is given for asymptotical stability of the null solution of an error dynamics. Finally, some numerical examples are provided to show the effectiveness of our results. Keywords—Adaptive function projective synchronization, Chaotic system, Lag synchronization, Lyapunov method
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