On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and Entropy
This paper introduces a novel fractional Ikeda-based memristor map and investigates its non-linear dynamics under commensurate and incommensurate orders using various numerical techniques, including Lyapunov exponent analysis, phase portraits, and bifurcation diagrams. The results reveal diverse and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/10/728 |
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| author | Omar Alsayyed Abderrahmane Abbes Gharib Mousa Gharib Mayada Abualhomos Hassan Al-Tarawneh Maha S. Al Soudi Nabeela Abu-Alkishik Abdallah Al-Husban Adel Ouannas |
| author_facet | Omar Alsayyed Abderrahmane Abbes Gharib Mousa Gharib Mayada Abualhomos Hassan Al-Tarawneh Maha S. Al Soudi Nabeela Abu-Alkishik Abdallah Al-Husban Adel Ouannas |
| author_sort | Omar Alsayyed |
| collection | DOAJ |
| description | This paper introduces a novel fractional Ikeda-based memristor map and investigates its non-linear dynamics under commensurate and incommensurate orders using various numerical techniques, including Lyapunov exponent analysis, phase portraits, and bifurcation diagrams. The results reveal diverse and complex system behaviors arising from the interplay of different fractional orders in the proposed map. Furthermore, the study employs the sample entropy test to quantify complexity and validate the presence of chaos. Non-linear controllers are also presented to stabilize and synchronize the model. The research emphasizes the system’s sensitivity to the fractional order parameters, leading to distinct dynamic patterns and stability regimes. The memristor-based chaotic map exhibits rich and intricate behavior, making it an interesting and important area of research. |
| first_indexed | 2024-03-10T21:13:58Z |
| format | Article |
| id | doaj.art-a5583c0c22d74408a1233adcfbba6042 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T21:13:58Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-a5583c0c22d74408a1233adcfbba60422023-11-19T16:34:26ZengMDPI AGFractal and Fractional2504-31102023-10-0171072810.3390/fractalfract7100728On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and EntropyOmar Alsayyed0Abderrahmane Abbes1Gharib Mousa Gharib2Mayada Abualhomos3Hassan Al-Tarawneh4Maha S. Al Soudi5Nabeela Abu-Alkishik6Abdallah Al-Husban7Adel Ouannas8Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, JordanLaboratory of Mathematics, Dynamics and Modelization, Badji Mokhtar-Annaba University, Annaba 23000, AlgeriaDepartment of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, JordanApplied Science Research Center (ASRC), Applied Science Private University, Amman 11942, JordanDepartment of Data Sciences and Artificial Intelligence, Al-Ahliyya Amman University, Amman 11942, JordanDepartment of Basic Scientific Sciences, Applied Science Private University, Amman 11931, JordanDepartment of Mathematics, Jerash University, Jerash 26150, JordanDepartment of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box 2600, Irbid 21110, JordanDepartment of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, AlgeriaThis paper introduces a novel fractional Ikeda-based memristor map and investigates its non-linear dynamics under commensurate and incommensurate orders using various numerical techniques, including Lyapunov exponent analysis, phase portraits, and bifurcation diagrams. The results reveal diverse and complex system behaviors arising from the interplay of different fractional orders in the proposed map. Furthermore, the study employs the sample entropy test to quantify complexity and validate the presence of chaos. Non-linear controllers are also presented to stabilize and synchronize the model. The research emphasizes the system’s sensitivity to the fractional order parameters, leading to distinct dynamic patterns and stability regimes. The memristor-based chaotic map exhibits rich and intricate behavior, making it an interesting and important area of research.https://www.mdpi.com/2504-3110/7/10/728Ikeda-based memristor mapdiscrete fractional calculusbifurcationchaotic dynamicssample entropycontrol |
| spellingShingle | Omar Alsayyed Abderrahmane Abbes Gharib Mousa Gharib Mayada Abualhomos Hassan Al-Tarawneh Maha S. Al Soudi Nabeela Abu-Alkishik Abdallah Al-Husban Adel Ouannas On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and Entropy Fractal and Fractional Ikeda-based memristor map discrete fractional calculus bifurcation chaotic dynamics sample entropy control |
| title | On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and Entropy |
| title_full | On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and Entropy |
| title_fullStr | On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and Entropy |
| title_full_unstemmed | On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and Entropy |
| title_short | On Ikeda-Based Memristor Map with Commensurate and Incommensurate Fractional Orders: Bifurcation, Chaos, and Entropy |
| title_sort | on ikeda based memristor map with commensurate and incommensurate fractional orders bifurcation chaos and entropy |
| topic | Ikeda-based memristor map discrete fractional calculus bifurcation chaotic dynamics sample entropy control |
| url | https://www.mdpi.com/2504-3110/7/10/728 |
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