{"title":"将具有控制参数的解析难解动力系统转化为可处理的金兹堡-朗道方程:几个例子","authors":"C. Kanchana, P. Siddheshwar","doi":"10.3126/nmsr.v35i1-2.29978","DOIUrl":null,"url":null,"abstract":"In the paper a means of making a simplified study of dynamical systems with a control parameter is presented. The intractable, third-order classical Lorenz system, the Lorenz-like Chen system and two topologically dissimilar fifth-order Lorenz systems are considered for illustration. Using the multi-scale method, these systems are reduced to an analytically tractable first-order Ginzburg-Landau equation (GLE) in one of the amplitudes. The analytical solution of the GLE is used to find the remaining amplitudes.","PeriodicalId":165940,"journal":{"name":"The Nepali Mathematical Sciences Report","volume":"40 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Transforming Analytically Intractable Dynamical Systems with a Control Parameter into a Tractable Ginzburg-Landau Equation: Few Illustrations\",\"authors\":\"C. Kanchana, P. Siddheshwar\",\"doi\":\"10.3126/nmsr.v35i1-2.29978\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the paper a means of making a simplified study of dynamical systems with a control parameter is presented. The intractable, third-order classical Lorenz system, the Lorenz-like Chen system and two topologically dissimilar fifth-order Lorenz systems are considered for illustration. Using the multi-scale method, these systems are reduced to an analytically tractable first-order Ginzburg-Landau equation (GLE) in one of the amplitudes. The analytical solution of the GLE is used to find the remaining amplitudes.\",\"PeriodicalId\":165940,\"journal\":{\"name\":\"The Nepali Mathematical Sciences Report\",\"volume\":\"40 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Nepali Mathematical Sciences Report\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3126/nmsr.v35i1-2.29978\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Nepali Mathematical Sciences Report","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3126/nmsr.v35i1-2.29978","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Transforming Analytically Intractable Dynamical Systems with a Control Parameter into a Tractable Ginzburg-Landau Equation: Few Illustrations
In the paper a means of making a simplified study of dynamical systems with a control parameter is presented. The intractable, third-order classical Lorenz system, the Lorenz-like Chen system and two topologically dissimilar fifth-order Lorenz systems are considered for illustration. Using the multi-scale method, these systems are reduced to an analytically tractable first-order Ginzburg-Landau equation (GLE) in one of the amplitudes. The analytical solution of the GLE is used to find the remaining amplitudes.
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