Special Fractional-Order Map and Its Realization

Amina-Aicha Khennaoui (), Adel Ouannas, Shaher Momani, Othman Abdullah Almatroud, Mohammed Mossa Al-Sawalha, Salah Mahmoud Boulaaras and Viet-Thanh Pham
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Amina-Aicha Khennaoui: Laboratory of Dynamical Systems and Control, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Adel Ouannas: Department of Mathematics and Computer Sciences, University of Larbi Ben M’hidi, Oum El Bouaghi 04000, Algeria
Shaher Momani: Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman 20550, United Arab Emirates
Othman Abdullah Almatroud: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Mohammed Mossa Al-Sawalha: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Salah Mahmoud Boulaaras: Department of Mathematics, College of Sciences and Arts in ArRass, Qassim University, Buraydah 51452, Saudi Arabia
Viet-Thanh Pham: Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam

Mathematics, 2022, vol. 10, issue 23, 1-11

Abstract: Recent works have focused the analysis of chaotic phenomena in fractional discrete memristor. However, most of the papers have been related to simulated results on the system dynamics rather than on their hardware implementations. This work reports the implementation of a new chaotic fractional memristor map with “hidden attractors”. The fractional memristor map is developed based on a memristive map by using the Grunwald–Letnikov difference operator. The fractional memristor map has flexible fixed points depending on a system’s parameters. We study system dynamics for different values of the fractional orders by using bifurcation diagrams, phase portraits, Lyapunov exponents, and the 0–1 test. We see that the fractional map generates rich dynamical behavior, including coexisting hidden dynamics and initial offset boosting.

Keywords: fractional map; chaos; discrete memristor; initial-boosting attractors (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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