Self-similarity techniques for chaotic attractors with many scrolls using step series switching

Highly applied in machining, image compressing, network traffic prediction, biological dynamics, nerve dendrite pattern and so on, self-similarity dynamic represents a part of fractal processes where an object is reproduced exactly or approximately exact to a part of itself. These reproduction proce...

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Autores principales:	Emile Franc Doungmo Goufo, Chokkalingam Ravichandran, Gunvant A. Birajdar
Formato:	article
Lenguaje:	EN
Publicado:	Vilnius Gediminas Technical University 2021
Materias:	mathematical and engineering model switching process self-organization fractal and fractional process numerical method Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/58fc3d128b034f9c84d7e445afe644f5
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spelling	oai:doaj.org-article:58fc3d128b034f9c84d7e445afe644f52021-11-29T09:14:00ZSelf-similarity techniques for chaotic attractors with many scrolls using step series switching1392-62921648-351010.3846/mma.2021.13678https://doaj.org/article/58fc3d128b034f9c84d7e445afe644f52021-11-01T00:00:00Zhttps://journals.vgtu.lt/index.php/MMA/article/view/13678https://doaj.org/toc/1392-6292https://doaj.org/toc/1648-3510Highly applied in machining, image compressing, network traffic prediction, biological dynamics, nerve dendrite pattern and so on, self-similarity dynamic represents a part of fractal processes where an object is reproduced exactly or approximately exact to a part of itself. These reproduction processes are also very important and captivating in chaos theory. They occur naturally in our environment in the form of growth spirals, romanesco broccoli, trees and so on. Seeking alternative ways to reproduce self-similarity dynamics has called the attention of many authors working in chaos theory since the range of applications is quite wide. In this paper, three combined notions, namely the step series switching process, the Julia’s technique and the fractal-fractional dynamic are used to create various forms of self-similarity dynamics in chaotic systems of attractors, initially with two, five and seven scrolls. In each case, the solvability of the model is addressed via numerical techniques and related graphical simulations are provided. It appears that the initial systems are able to trigger a self-similarity process that generates the exact or approximately exact copy of itself or part of itself. Moreover, the dynamics of the copies are impacted by some model’s parameters involved in the process. Using mathematical concepts to re-create features that usually occur in a natural way proves to be a prowess as related applications are many for engineers.Emile Franc Doungmo GoufoChokkalingam RavichandranGunvant A. BirajdarVilnius Gediminas Technical Universityarticlemathematical and engineering modelswitching processself-organizationfractal and fractional processnumerical methodMathematicsQA1-939ENMathematical Modelling and Analysis, Vol 26, Iss 4, Pp 591-611 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	mathematical and engineering model switching process self-organization fractal and fractional process numerical method Mathematics QA1-939
spellingShingle	mathematical and engineering model switching process self-organization fractal and fractional process numerical method Mathematics QA1-939 Emile Franc Doungmo Goufo Chokkalingam Ravichandran Gunvant A. Birajdar Self-similarity techniques for chaotic attractors with many scrolls using step series switching
description	Highly applied in machining, image compressing, network traffic prediction, biological dynamics, nerve dendrite pattern and so on, self-similarity dynamic represents a part of fractal processes where an object is reproduced exactly or approximately exact to a part of itself. These reproduction processes are also very important and captivating in chaos theory. They occur naturally in our environment in the form of growth spirals, romanesco broccoli, trees and so on. Seeking alternative ways to reproduce self-similarity dynamics has called the attention of many authors working in chaos theory since the range of applications is quite wide. In this paper, three combined notions, namely the step series switching process, the Julia’s technique and the fractal-fractional dynamic are used to create various forms of self-similarity dynamics in chaotic systems of attractors, initially with two, five and seven scrolls. In each case, the solvability of the model is addressed via numerical techniques and related graphical simulations are provided. It appears that the initial systems are able to trigger a self-similarity process that generates the exact or approximately exact copy of itself or part of itself. Moreover, the dynamics of the copies are impacted by some model’s parameters involved in the process. Using mathematical concepts to re-create features that usually occur in a natural way proves to be a prowess as related applications are many for engineers.
format	article
author	Emile Franc Doungmo Goufo Chokkalingam Ravichandran Gunvant A. Birajdar
author_facet	Emile Franc Doungmo Goufo Chokkalingam Ravichandran Gunvant A. Birajdar
author_sort	Emile Franc Doungmo Goufo
title	Self-similarity techniques for chaotic attractors with many scrolls using step series switching
title_short	Self-similarity techniques for chaotic attractors with many scrolls using step series switching
title_full	Self-similarity techniques for chaotic attractors with many scrolls using step series switching
title_fullStr	Self-similarity techniques for chaotic attractors with many scrolls using step series switching
title_full_unstemmed	Self-similarity techniques for chaotic attractors with many scrolls using step series switching
title_sort	self-similarity techniques for chaotic attractors with many scrolls using step series switching
publisher	Vilnius Gediminas Technical University
publishDate	2021
url	https://doaj.org/article/58fc3d128b034f9c84d7e445afe644f5
work_keys_str_mv	AT emilefrancdoungmogoufo selfsimilaritytechniquesforchaoticattractorswithmanyscrollsusingstepseriesswitching AT chokkalingamravichandran selfsimilaritytechniquesforchaoticattractorswithmanyscrollsusingstepseriesswitching AT gunvantabirajdar selfsimilaritytechniquesforchaoticattractorswithmanyscrollsusingstepseriesswitching
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Self-similarity techniques for chaotic attractors with many scrolls using step series switching

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