Numerical study of a nonlinear fractional chaotic Chua's circuit
As an exponentially growing sensitivity to modest perturbations, chaos is pervasive in nature. Chaos is expected to provide a variety of functional purposes in both technological and biological systems. This work applies the time-fractional Caputo and Caputo-Fabrizio fractional derivatives to the Ch...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023083?viewType=HTML |
| _version_ | 1811323654524370944 |
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| author | Nehad Ali Shah Iftikhar Ahmed Kanayo K. Asogwa Azhar Ali Zafar Wajaree Weera Ali Akgül |
| author_facet | Nehad Ali Shah Iftikhar Ahmed Kanayo K. Asogwa Azhar Ali Zafar Wajaree Weera Ali Akgül |
| author_sort | Nehad Ali Shah |
| collection | DOAJ |
| description | As an exponentially growing sensitivity to modest perturbations, chaos is pervasive in nature. Chaos is expected to provide a variety of functional purposes in both technological and biological systems. This work applies the time-fractional Caputo and Caputo-Fabrizio fractional derivatives to the Chua type nonlinear chaotic systems. A numerical analysis of the mathematical models is used to compare the chaotic behavior of systems with differential operators of integer order versus systems with fractional differential operators. Even though the chaotic behavior of the classical Chua's circuit has been extensively investigated, our generalization can highlight new aspects of system behavior and the effects of memory on the evolution of the chaotic generalized circuit. |
| first_indexed | 2024-04-13T13:59:00Z |
| format | Article |
| id | doaj.art-c9844e07010c406e9756322d136f68a2 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-13T13:59:00Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-c9844e07010c406e9756322d136f68a22022-12-22T02:44:06ZengAIMS PressAIMS Mathematics2473-69882023-01-01811636165510.3934/math.2023083Numerical study of a nonlinear fractional chaotic Chua's circuitNehad Ali Shah0Iftikhar Ahmed1Kanayo K. Asogwa2Azhar Ali Zafar3Wajaree Weera4Ali Akgül51. Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea2. Department of Mathematics & Statistics, University of Swat, Khyber Pukhtoonkhwa, Pakistan3. Department of Mathematics, Nigeria Maritime University, Okerenkoko, Delta State, Nigeria4. Department of Mathematics, GC University Lahore, Lahore, Pakistan5. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand6. Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt Turkey 7. Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia /Mersin 10-TurkeyAs an exponentially growing sensitivity to modest perturbations, chaos is pervasive in nature. Chaos is expected to provide a variety of functional purposes in both technological and biological systems. This work applies the time-fractional Caputo and Caputo-Fabrizio fractional derivatives to the Chua type nonlinear chaotic systems. A numerical analysis of the mathematical models is used to compare the chaotic behavior of systems with differential operators of integer order versus systems with fractional differential operators. Even though the chaotic behavior of the classical Chua's circuit has been extensively investigated, our generalization can highlight new aspects of system behavior and the effects of memory on the evolution of the chaotic generalized circuit.https://www.aimspress.com/article/doi/10.3934/math.2023083?viewType=HTMLchaosnonlinear chaotic systemscaputo and caputo-fabrizio fractional derivativeschaotic generalized circuit |
| spellingShingle | Nehad Ali Shah Iftikhar Ahmed Kanayo K. Asogwa Azhar Ali Zafar Wajaree Weera Ali Akgül Numerical study of a nonlinear fractional chaotic Chua's circuit AIMS Mathematics chaos nonlinear chaotic systems caputo and caputo-fabrizio fractional derivatives chaotic generalized circuit |
| title | Numerical study of a nonlinear fractional chaotic Chua's circuit |
| title_full | Numerical study of a nonlinear fractional chaotic Chua's circuit |
| title_fullStr | Numerical study of a nonlinear fractional chaotic Chua's circuit |
| title_full_unstemmed | Numerical study of a nonlinear fractional chaotic Chua's circuit |
| title_short | Numerical study of a nonlinear fractional chaotic Chua's circuit |
| title_sort | numerical study of a nonlinear fractional chaotic chua s circuit |
| topic | chaos nonlinear chaotic systems caputo and caputo-fabrizio fractional derivatives chaotic generalized circuit |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023083?viewType=HTML |
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