Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points

Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points

This paper starts with a review of three-dimensional chaotic dynamical systems equipped with special curves of balance points. We also propose the mathematical model of a new three-dimensional chaotic system equipped with a closed butterfly-like curve of balance points. By performing a bifurcation s...

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Main Authors: Aceng Sambas, Sundarapandian Vaidyanathan, Talal Bonny, Sen Zhang, Sukono, Yuyun Hidayat, Gugun Gundara, Mustafa Mamat
Format: Article
Language:English
Published: MDPI AG 2021-01-01
Series:Applied Sciences
Subjects:
chaotic systems
chaos
multi-stability
transient chaos
FPGA implementation
Online Access:https://www.mdpi.com/2076-3417/11/2/788
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spelling doaj-64700b4119384c43bf8e5fe9e74601af2021-01-16T00:03:15ZengMDPI AGApplied Sciences2076-34172021-01-011178878810.3390/app11020788Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium PointsAceng Sambas0Sundarapandian Vaidyanathan1Talal Bonny2Sen Zhang3Sukono4Yuyun Hidayat5Gugun Gundara6Mustafa Mamat7Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196, IndonesiaCentre for Control Systems, Vel Tech University, Vel Nagar, Avadi, Chennai 600 062, IndiaDepartment of Computer Engineering, University of Sharjah, Sharjah 26666, UAESchool of Physics and Opotoelectric Engineering, Xiangtan University, Xiangtan 411105, ChinaDepartment of Mathematics, Universitas Padjadjaran, Jatinangor, Kabupaten Sumedang 45363, IndonesiaDepartment of Statistics, Universitas Padjadjaran, Jatinangor, Kabupaten Sumedang 45363, IndonesiaDepartment of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196, IndonesiaFaculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Gong Badak, Kuala Terengganu 21300, MalaysiaThis paper starts with a review of three-dimensional chaotic dynamical systems equipped with special curves of balance points. We also propose the mathematical model of a new three-dimensional chaotic system equipped with a closed butterfly-like curve of balance points. By performing a bifurcation study of the new system, we analyze intrinsic properties such as chaoticity, multi-stability, and transient chaos. Finally, we carry out a realization of the new multi-stable chaotic model using Field-Programmable Gate Array (FPGA).https://www.mdpi.com/2076-3417/11/2/788chaotic systemschaosmulti-stabilitytransient chaosFPGA implementation
collection DOAJ
language English
format Article
sources DOAJ
author Aceng Sambas
Sundarapandian Vaidyanathan
Talal Bonny
Sen Zhang
Sukono
Yuyun Hidayat
Gugun Gundara
Mustafa Mamat
spellingShingle Aceng Sambas
Sundarapandian Vaidyanathan
Talal Bonny
Sen Zhang
Sukono
Yuyun Hidayat
Gugun Gundara
Mustafa Mamat
Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points
Applied Sciences
chaotic systems
chaos
multi-stability
transient chaos
FPGA implementation
author_facet Aceng Sambas
Sundarapandian Vaidyanathan
Talal Bonny
Sen Zhang
Sukono
Yuyun Hidayat
Gugun Gundara
Mustafa Mamat
author_sort Aceng Sambas
title Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points
title_short Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points
title_full Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points
title_fullStr Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points
title_full_unstemmed Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points
title_sort mathematical model and fpga realization of a multi-stable chaotic dynamical system with a closed butterfly-like curve of equilibrium points
publisher MDPI AG
series Applied Sciences
issn 2076-3417
publishDate 2021-01-01
description This paper starts with a review of three-dimensional chaotic dynamical systems equipped with special curves of balance points. We also propose the mathematical model of a new three-dimensional chaotic system equipped with a closed butterfly-like curve of balance points. By performing a bifurcation study of the new system, we analyze intrinsic properties such as chaoticity, multi-stability, and transient chaos. Finally, we carry out a realization of the new multi-stable chaotic model using Field-Programmable Gate Array (FPGA).
topic chaotic systems
chaos
multi-stability
transient chaos
FPGA implementation
url https://www.mdpi.com/2076-3417/11/2/788
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