{"title":"Rössler系统中双螺旋同斜轨道的周期1运动","authors":"","doi":"10.1115/1.4062201","DOIUrl":null,"url":null,"abstract":"\n In this paper, period-1 motions to twin spiral homoclinic orbits in the Rossler system are presented. The period-1 motions varying with a systems parameter are predicted semi-analytically through an implicit mapping method, and the corresponding stability and bifurcations of the period-1 motions are determined through eigenvalue analysis. The approximate homoclinic orbits are obtained, which can be detected through the periodic motions with the positive and negative infinite large eigenvalues. The two limit ends of the bifurcation diagram of the period-1 motion are at twin spiral homoclinic orbits. For comparison, numerical and analytical results of stable period-1 motion are presented. The approximate spiral homoclinic orbits are demonstrated for a better understanding of complex dynamics of homoclinic orbits. Herein, only initial results on periodic motions to homoclinic orbits are presented for the Rossler system. In fact, the Rossler system has rich complex dynamics existing in other high-dimensional nonlinear systems. Thus, the further studies of bifurcation trees of periodic motions to infinite homoclinic orbits will be completed in sequel.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"2 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Period-1 Motions to Twin Spiral Homoclinic Orbits in the Rössler System\",\"authors\":\"\",\"doi\":\"10.1115/1.4062201\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n In this paper, period-1 motions to twin spiral homoclinic orbits in the Rossler system are presented. The period-1 motions varying with a systems parameter are predicted semi-analytically through an implicit mapping method, and the corresponding stability and bifurcations of the period-1 motions are determined through eigenvalue analysis. The approximate homoclinic orbits are obtained, which can be detected through the periodic motions with the positive and negative infinite large eigenvalues. The two limit ends of the bifurcation diagram of the period-1 motion are at twin spiral homoclinic orbits. For comparison, numerical and analytical results of stable period-1 motion are presented. The approximate spiral homoclinic orbits are demonstrated for a better understanding of complex dynamics of homoclinic orbits. Herein, only initial results on periodic motions to homoclinic orbits are presented for the Rossler system. In fact, the Rossler system has rich complex dynamics existing in other high-dimensional nonlinear systems. Thus, the further studies of bifurcation trees of periodic motions to infinite homoclinic orbits will be completed in sequel.\",\"PeriodicalId\":54858,\"journal\":{\"name\":\"Journal of Computational and Nonlinear Dynamics\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2023-03-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Nonlinear Dynamics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4062201\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Nonlinear Dynamics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1115/1.4062201","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Period-1 Motions to Twin Spiral Homoclinic Orbits in the Rössler System
In this paper, period-1 motions to twin spiral homoclinic orbits in the Rossler system are presented. The period-1 motions varying with a systems parameter are predicted semi-analytically through an implicit mapping method, and the corresponding stability and bifurcations of the period-1 motions are determined through eigenvalue analysis. The approximate homoclinic orbits are obtained, which can be detected through the periodic motions with the positive and negative infinite large eigenvalues. The two limit ends of the bifurcation diagram of the period-1 motion are at twin spiral homoclinic orbits. For comparison, numerical and analytical results of stable period-1 motion are presented. The approximate spiral homoclinic orbits are demonstrated for a better understanding of complex dynamics of homoclinic orbits. Herein, only initial results on periodic motions to homoclinic orbits are presented for the Rossler system. In fact, the Rossler system has rich complex dynamics existing in other high-dimensional nonlinear systems. Thus, the further studies of bifurcation trees of periodic motions to infinite homoclinic orbits will be completed in sequel.
期刊介绍:
The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.