An effective numerical method for simulating a class of fractional-order chaotic system

Hai Yan Zhang; Wei Zhang; Hai Yan Zhang; Wei Zhang

doi:10.3934/nhm.2025047

Networks and Heterogeneous Media

2025, Volume 20, Issue 4: 1087-1107. doi: 10.3934/nhm.2025047

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Research article

An effective numerical method for simulating a class of fractional-order chaotic system

Hai Yan Zhang ¹,
Wei Zhang ^{2
,
,}

1.
School of Physics and Electronic Information Engineering, Jining Normal University, Ulanqab, Inner Mongolia 012000, China
2.
Institute of Economics and Management, Jining Normal University, Ulanqab, Inner Mongolia 012000, China

Received: 09 August 2025 Revised: 24 September 2025 Accepted: 10 October 2025 Published: 21 October 2025

This paper investigates the chaotic dynamics and control of fractional-order chaotic systems. A high-precision numerical method based on the Grünwald–Letnikov definition is developed to explore the system's dynamics. We also design linear feedback and adaptive control strategies to achieve chaotic synchronization and system stabilization. Numerical simulations validate the effectiveness of our methods, showing successful synchronization and control of the chaotic system.
- numerical method,
- stability analysis,
- adaptive control,
- fractional-order chaotic system
Citation: Hai Yan Zhang, Wei Zhang. An effective numerical method for simulating a class of fractional-order chaotic system[J]. Networks and Heterogeneous Media, 2025, 20(4): 1087-1107. doi: 10.3934/nhm.2025047

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Abstract

This paper investigates the chaotic dynamics and control of fractional-order chaotic systems. A high-precision numerical method based on the Grünwald–Letnikov definition is developed to explore the system's dynamics. We also design linear feedback and adaptive control strategies to achieve chaotic synchronization and system stabilization. Numerical simulations validate the effectiveness of our methods, showing successful synchronization and control of the chaotic system.

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