Chaos control in discrete fractional systems with variable order: analysis and numerical simulations

Omar Kahouli; Noureddine Djenina; Adel Ouannas; Badr M. Alshammari; Ali Aloui; Ilyes Abidi; Omar Kahouli; Noureddine Djenina; Adel Ouannas; Badr M. Alshammari; Ali Aloui; Ilyes Abidi

doi:10.3934/era.2026004

Electronic Research Archive

2026, Volume 34, Issue 1: 55-68. doi: 10.3934/era.2026004

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Chaos control in discrete fractional systems with variable order: analysis and numerical simulations

1.
Department of Electronics Engineering, Applied College, University of Ha’il, Ha’il 2440, Saudi Arabia
2.
Institute of Hygiene and Safety, University of Batna 2, Fesdis, Batna 05078, Algeria
3.
Department of Mathematics and Computer Science, University of Oum EL-Bouaghi, Oum El Bouaghi 04000, Algeria
4.
Department of Electrical Engineering, College of Engineering, University of Ha’il, Ha’il 2440, Saudi Arabia
5.
Management Information Systems Department, Applied College, University of Ha’il, Ha’il 2440, Saudi Arabia

Received: 02 October 2025 Revised: 18 December 2025 Accepted: 22 December 2025 Published: 29 December 2025

This study investigates how to control chaos in discrete-time systems that have variable fractional orders. We examine a general type of discrete fractional-order equations where the order changes with time, and we show that these systems can become chaotic when certain parameters are chosen. To address this, we develop and apply tailored control techniques to suppress chaos and achieve system stabilization. Using detailed numerical simulations, we confirm that the suggested control method works effectively in two example cases. Our findings underscore that chaos control in variable fractional-order systems provides significant flexibility in modulating dynamic behavior, offering valuable insights into the broader applicability of these methods in discrete fractional-order systems.
- chaos,
- control,
- Lorenz system,
- sine-based memristor map,
- discrete systems,
- fractional order,
- variable order
Citation: Omar Kahouli, Noureddine Djenina, Adel Ouannas, Badr M. Alshammari, Ali Aloui, Ilyes Abidi. Chaos control in discrete fractional systems with variable order: analysis and numerical simulations[J]. Electronic Research Archive, 2026, 34(1): 55-68. doi: 10.3934/era.2026004

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Abstract

This study investigates how to control chaos in discrete-time systems that have variable fractional orders. We examine a general type of discrete fractional-order equations where the order changes with time, and we show that these systems can become chaotic when certain parameters are chosen. To address this, we develop and apply tailored control techniques to suppress chaos and achieve system stabilization. Using detailed numerical simulations, we confirm that the suggested control method works effectively in two example cases. Our findings underscore that chaos control in variable fractional-order systems provides significant flexibility in modulating dynamic behavior, offering valuable insights into the broader applicability of these methods in discrete fractional-order systems.

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