The New Four-Dimensional Fractional Chaotic Map with Constant and Variable-Order: Chaos, Control and Synchronization

Tareq Hamadneh, Souad Bensid Ahmed, Hassan Al-Tarawneh, Omar Alsayyed, Gharib Mousa Gharib, Maha S. Al Soudi, Abderrahmane Abbes () and Adel Ouannas
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Tareq Hamadneh: Department of Mathematics, Faculty of Science, Al Zaytoonah University of Jordan, Amman 11931, Jordan
Souad Bensid Ahmed: Department of Mathematics, The University of Jordan, Amman 11942, Jordan
Hassan Al-Tarawneh: Department of Data Sciences and Artificial Intelligence, Al-Ahliyya Amman University, Amman 11942, Jordan
Omar Alsayyed: Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan
Gharib Mousa Gharib: Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
Maha S. Al Soudi: Department of Basic Scientific Sciences, Applied Science Private University, Amman 11942, Jordan
Abderrahmane Abbes: Laboratory of Mathematics, Dynamics and Modelization, Badji Mokhtar-Annaba University, Annaba 23000, Algeria
Adel Ouannas: Department of Mathematics and Computer Science, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria

Mathematics, 2023, vol. 11, issue 20, 1-19

Abstract: Using fractional difference equations to describe fractional and variable-order maps, this manuscript discusses the dynamics of the discrete 4D sinusoidal feedback sine iterative chaotic map with infinite collapse (ICMIC) modulation map (SF-SIMM) with fractional-order. Also, it presents a novel variable-order version of SF-SIMM and discusses their chaotic dynamic behavior by employing a distinct function for the variable fractional-order. To establish the existence of chaos in the suggested discrete SF-SIMM, some numerical methods such as phase plots, bifurcation and largest Lyapunov exponent diagrams, C 0 complexity and 0–1 test are utilized. After that, two different control schemes are used for the conceived discrete system. The states are stabilized and asymptotically forced towards zero by the first controller. The second controller is used to synchronize a pair of maps with non–identical parameters. Finally, MATLAB simulations will be executed to confirm the results provided.

Keywords: variable fractional-order; dynamical behavior; chaos; C 0 complexity; largest Lyapunov exponents (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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