{"title":"Density-Colored Bifurcation Diagrams — A Complementary Tool for Chaotic Map Analysis","authors":"L. Moysis, M. Lawnik, Christos Volos","doi":"10.1142/s0218127423300367","DOIUrl":null,"url":null,"abstract":"This work presents a numerical method to color the bifurcation diagram of any discrete map, based on the distribution of the map’s values in its domain. This density-colored diagram reveals information on the uniformity of the map’s value distribution across its domain set, as a bifurcation parameter is increased. This diagram can serve as a complementary visual tool for the analysis of chaotic maps, and can be vital for the application of chaotic dynamics.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"155 3","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Bifurcation and Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0218127423300367","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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Abstract
This work presents a numerical method to color the bifurcation diagram of any discrete map, based on the distribution of the map’s values in its domain. This density-colored diagram reveals information on the uniformity of the map’s value distribution across its domain set, as a bifurcation parameter is increased. This diagram can serve as a complementary visual tool for the analysis of chaotic maps, and can be vital for the application of chaotic dynamics.
期刊介绍：
The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering.
The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.
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