{"title":"单模系统中的三频共振","authors":"A. Nimets, D. Vavriv, K. Schuenemann","doi":"10.1109/MSMW.2016.7538197","DOIUrl":null,"url":null,"abstract":"We review recent results on the interaction of low- and high-frequency oscillations that lead to arising of three-frequency resonances in nonlinear oscillators. The Duffing oscillator and the Van der Pol oscillator both with modulated natural frequency and a high-frequency harmonic forcing are considered as examples to illustrate and study this phenomenon. It is shown that such interaction enables an efficient control of the oscillators dynamics and their properties. The formation of bistable states and synchronous oscillations is considered in detail.","PeriodicalId":6504,"journal":{"name":"2016 9th International Kharkiv Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves (MSMW)","volume":"14 1","pages":"1-4"},"PeriodicalIF":0.0000,"publicationDate":"2016-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Three-frequency resonances in single-mode systems\",\"authors\":\"A. Nimets, D. Vavriv, K. Schuenemann\",\"doi\":\"10.1109/MSMW.2016.7538197\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We review recent results on the interaction of low- and high-frequency oscillations that lead to arising of three-frequency resonances in nonlinear oscillators. The Duffing oscillator and the Van der Pol oscillator both with modulated natural frequency and a high-frequency harmonic forcing are considered as examples to illustrate and study this phenomenon. It is shown that such interaction enables an efficient control of the oscillators dynamics and their properties. The formation of bistable states and synchronous oscillations is considered in detail.\",\"PeriodicalId\":6504,\"journal\":{\"name\":\"2016 9th International Kharkiv Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves (MSMW)\",\"volume\":\"14 1\",\"pages\":\"1-4\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2016 9th International Kharkiv Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves (MSMW)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MSMW.2016.7538197\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2016 9th International Kharkiv Symposium on Physics and Engineering of Microwaves, Millimeter and Submillimeter Waves (MSMW)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MSMW.2016.7538197","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们回顾了导致非线性振荡器中出现三频共振的低频和高频振荡相互作用的最新结果。以具有调制固有频率和高频谐波强迫的Duffing振子和Van der Pol振子为例来说明和研究这一现象。结果表明，这种相互作用可以有效地控制振子的动力学和特性。详细讨论了双稳态和同步振荡的形成。
We review recent results on the interaction of low- and high-frequency oscillations that lead to arising of three-frequency resonances in nonlinear oscillators. The Duffing oscillator and the Van der Pol oscillator both with modulated natural frequency and a high-frequency harmonic forcing are considered as examples to illustrate and study this phenomenon. It is shown that such interaction enables an efficient control of the oscillators dynamics and their properties. The formation of bistable states and synchronous oscillations is considered in detail.
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