Title: Chaos control strategies for a novel fractional order four-dimensional chaotic system

Authors: R.N. Premakumari; Chandrali Baishya; Manisha Krishna Naik

Addresses: Department of Mathematics, M.E.S. Degree College of Arts, Commerce and Science, Malleswaram, Bangalore – 560003, Karnataka, India ' Department of Studies and Research in Mathematics, Tumkur University, Jnanasiri Campus, Tumakuru – 572118, Karnataka, India ' Department of Mathematics, SJBIT, Bengalore – 560060, Karnataka, India

Abstract: Studying chaotic systems is beneficial as it enhances our understanding of complex dynamics, with significant implications across philosophy, technology, and science. In this work, we introduce a novel four-dimensional (4D) chaotic system within the framework of the Caputo fractional derivative. Various tools reveal that its dynamics differ from other existing 4D chaotic systems. This model, incorporating the fractional derivative, offers a more accurate description of the system's memory effect and non-local behaviour. Calculating the Lyapunov exponent values for various fractional orders, we confirm the chaotic nature of the proposed model. We study dynamical features such as dissipation, the existence and uniqueness of solutions, equilibrium points, and linear stability through theoretical analysis. Our goal is to regulate the chaos in the system, achieved by designing two distinct sliding mode controllers. Their efficacy, especially under external disturbances and uncertainties, is observed in both commensurate and incommensurate systems, and validated through numerical simulations.

Keywords: chaos; a new 4D chaotic system; Caputo fractional derivative; sliding mode controller; predictor-corrector method.

DOI: 10.1504/IJANS.2024.146675

International Journal of Applied Nonlinear Science, 2024 Vol.4 No.4, pp.283 - 307

Received: 30 Jan 2024
Accepted: 22 Jun 2024
Published online: 11 Jun 2025 *

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