{"title":"光纤中具有时空导数的分数阶摄动Chen-Lee-Liu模型的分岔、相位肖像、混沌模式和行波解","authors":"Zhao Li","doi":"10.1142/s0218348x23401928","DOIUrl":null,"url":null,"abstract":"In this paper, the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is under consideration. First, the traveling wave transformation is applied to transform the fractional perturbed Chen–Lee–Liu model into two-dimensional planar dynamic systems. Second, the bifurcation of the dynamics system of the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is discussed by using the theory of the plane dynamics systems. Finally, the traveling wave solutions of the fractional perturbed Chen–Lee–Liu model are obtained via the analysis method of planar dynamical system.","PeriodicalId":55144,"journal":{"name":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","volume":"219 1","pages":"0"},"PeriodicalIF":3.3000,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Bifurcation, phase portrait, chaotic pattern and traveling wave solution of the fractional perturbed Chen-Lee-Liu model with beta time-space derivative in fiber optics\",\"authors\":\"Zhao Li\",\"doi\":\"10.1142/s0218348x23401928\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is under consideration. First, the traveling wave transformation is applied to transform the fractional perturbed Chen–Lee–Liu model into two-dimensional planar dynamic systems. Second, the bifurcation of the dynamics system of the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is discussed by using the theory of the plane dynamics systems. Finally, the traveling wave solutions of the fractional perturbed Chen–Lee–Liu model are obtained via the analysis method of planar dynamical system.\",\"PeriodicalId\":55144,\"journal\":{\"name\":\"Fractals-Complex Geometry Patterns and Scaling in Nature and Society\",\"volume\":\"219 1\",\"pages\":\"0\"},\"PeriodicalIF\":3.3000,\"publicationDate\":\"2023-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractals-Complex Geometry Patterns and Scaling in Nature and Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218348x23401928\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractals-Complex Geometry Patterns and Scaling in Nature and Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218348x23401928","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Bifurcation, phase portrait, chaotic pattern and traveling wave solution of the fractional perturbed Chen-Lee-Liu model with beta time-space derivative in fiber optics
In this paper, the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is under consideration. First, the traveling wave transformation is applied to transform the fractional perturbed Chen–Lee–Liu model into two-dimensional planar dynamic systems. Second, the bifurcation of the dynamics system of the fractional perturbed Chen–Lee–Liu model with beta time-space derivative is discussed by using the theory of the plane dynamics systems. Finally, the traveling wave solutions of the fractional perturbed Chen–Lee–Liu model are obtained via the analysis method of planar dynamical system.
期刊介绍：
The investigation of phenomena involving complex geometry, patterns and scaling has gone through a spectacular development and applications in the past decades. For this relatively short time, geometrical and/or temporal scaling have been shown to represent the common aspects of many processes occurring in an unusually diverse range of fields including physics, mathematics, biology, chemistry, economics, engineering and technology, and human behavior. As a rule, the complex nature of a phenomenon is manifested in the underlying intricate geometry which in most of the cases can be described in terms of objects with non-integer (fractal) dimension. In other cases, the distribution of events in time or various other quantities show specific scaling behavior, thus providing a better understanding of the relevant factors determining the given processes.
Using fractal geometry and scaling as a language in the related theoretical, numerical and experimental investigations, it has been possible to get a deeper insight into previously intractable problems. Among many others, a better understanding of growth phenomena, turbulence, iterative functions, colloidal aggregation, biological pattern formation, stock markets and inhomogeneous materials has emerged through the application of such concepts as scale invariance, self-affinity and multifractality.
The main challenge of the journal devoted exclusively to the above kinds of phenomena lies in its interdisciplinary nature; it is our commitment to bring together the most recent developments in these fields so that a fruitful interaction of various approaches and scientific views on complex spatial and temporal behaviors in both nature and society could take place.
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