Bifurcation, Hidden Chaos, Entropy and Control in Hénon-Based Fractional Memristor Map with Commensurate and Incommensurate Orders

Mayada Abualhomos, Abderrahmane Abbes (), Gharib Mousa Gharib, Abdallah Shihadeh, Maha S. Al Soudi, Ahmed Atallah Alsaraireh and Adel Ouannas
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Mayada Abualhomos: Applied Science Research Center (ASRC), Applied Science Private University, Amman 11942, Jordan
Abderrahmane Abbes: Laboratory of Mathematics, Dynamics and Modelization, Badji Mokhtar-Annaba University, Annaba 23000, Algeria
Gharib Mousa Gharib: Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
Abdallah Shihadeh: Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan
Maha S. Al Soudi: Department of Basic Scientific Sciences, Applied Science Private University, Amman 11931, Jordan
Ahmed Atallah Alsaraireh: Department of Computer Information Systems, The University of Jordan, Amman 11942, Jordan
Adel Ouannas: Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria

Mathematics, 2023, vol. 11, issue 19, 1-19

Abstract: In this paper, we present an innovative 3D fractional Hénon-based memristor map and conduct an extensive exploration and analysis of its dynamic behaviors under commensurate and incommensurate orders. The study employs diverse numerical techniques, such as visualizing phase portraits, analyzing Lyapunov exponents, plotting bifurcation diagrams, and applying the sample entropy test to assess the complexity and validate the chaotic characteristics. However, since the proposed fractional map has no fixed points, the outcomes reveal that the map can exhibit a wide range of hidden dynamical behaviors. This phenomenon significantly augments the complexity of the fractal structure inherent to the chaotic attractors. Moreover, we introduce nonlinear controllers designed for stabilizing and synchronizing the proposed fractional Hénon-based memristor map. The research emphasizes the system’s sensitivity to fractional-order parameters, resulting in the emergence of distinct dynamic patterns. The memristor-based chaotic map exhibits rich and intricate behavior, making it a captivating and significant area of investigation.

Keywords: Hénon-based map; memristor; discrete fractional calculus; chaotic dynamics; entropy; control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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