{"title":"二流体磁化等离子体振荡器在参数激励下的轨道和混沌","authors":"Sengen Hu, Liangqiang Zhou","doi":"10.1002/zamm.202300441","DOIUrl":null,"url":null,"abstract":"Abstract In this manuscript, a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback is studied both analytically and numerically. The Hamilton systems of triple‐well and narrow single‐well are discussed in detail. The scenarios of phase portraits and equilibria are given. Homoclinic and heteroclinic orbits are strictly derived. With the Melnikov method, the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically. We have discovered some interesting dynamic phenomena, such as uncontrollable time delays with which chaos always occurs for this system. The influence of time‐delay on the chaotic property is also studied rigorously. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré sections, Lyapunov exponential spectrums and attractor basins are given. Numerical simulations are consistent with theoretical results.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"175 1","pages":"0"},"PeriodicalIF":2.3000,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback\",\"authors\":\"Sengen Hu, Liangqiang Zhou\",\"doi\":\"10.1002/zamm.202300441\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this manuscript, a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback is studied both analytically and numerically. The Hamilton systems of triple‐well and narrow single‐well are discussed in detail. The scenarios of phase portraits and equilibria are given. Homoclinic and heteroclinic orbits are strictly derived. With the Melnikov method, the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically. We have discovered some interesting dynamic phenomena, such as uncontrollable time delays with which chaos always occurs for this system. The influence of time‐delay on the chaotic property is also studied rigorously. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré sections, Lyapunov exponential spectrums and attractor basins are given. Numerical simulations are consistent with theoretical results.\",\"PeriodicalId\":23924,\"journal\":{\"name\":\"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik\",\"volume\":\"175 1\",\"pages\":\"0\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2023-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1002/zamm.202300441\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1002/zamm.202300441","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback
Abstract In this manuscript, a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback is studied both analytically and numerically. The Hamilton systems of triple‐well and narrow single‐well are discussed in detail. The scenarios of phase portraits and equilibria are given. Homoclinic and heteroclinic orbits are strictly derived. With the Melnikov method, the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically. We have discovered some interesting dynamic phenomena, such as uncontrollable time delays with which chaos always occurs for this system. The influence of time‐delay on the chaotic property is also studied rigorously. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré sections, Lyapunov exponential spectrums and attractor basins are given. Numerical simulations are consistent with theoretical results.
期刊介绍:
ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.