Title: Mathematical modelling, bifurcation analysis, circuit design and FPGA implementation of a 5D hyperchaotic weather fluctuation model with a line of equilibrium points

Authors: Sundarapandian Vaidyanathan; Irene M. Moroz; Esteban Tlelo-Cuautle; Aceng Sambas; Ciro Fabian Bermudez-Marquez; Samy Abdelwahab Safaan

Addresses: Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Avadi, Chennai – 600062, Tamil Nadu, India ' Mathematical Institute, University of Oxford, Oxford OX2 6GG, England, UK ' Department of Electronics, The National Institute of Astrophysics, Optics and Electronics (INAOE), Tonantzintla, Puebla 72840, Mexico ' Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya 46196, West Java, Indonesia ' Department of Electronics, The National Institute of Astrophysics, Optics and Electronics (INAOE), Tonantzintla, Puebla 72840, Mexico ' Department of Natural and Applied Sciences, Community College of Buraydah, Qassim University, Buraydah, 52571, Saudi Arabia; Nile Higher Institute for Commercial Science and Computer Technology, Mansoura, 35511, Egypt

Abstract: High-dimensional hyperchaotic systems are known to have several applications in engineering owing to their high complexity. This work reports the finding of a new 5D hyperchaotic weather fluctuation model, which is constructed by means of introducing two state feedback controllers in the 3D Vallis weather fluctuation model (1986). The new hyperchaotic system has a line of equilibrium points. Hence, it has hidden attractors. We carry out a detailed bifurcation analysis with standard tools such as bifurcation diagrams and Lyapunov exponents to study the intrinsic properties of the 5D weather fluctuation model with respect to changes in the system constants. Next, we design an electronic circuit of the 5D weather fluctuation model using MultiSim. The new 5D hyperchaotic weather fluctuation model is implemented herein by applying two one-step numerical methods, viz., forward Euler and trapezoidal rule. Experimental attractors for the 5D hyperchaotic model are shown from an oscilloscope.

Keywords: modelling; bifurcation; chaos; hyperchaos; hyperchaotic systems; equilibrium points; line equilibrium; stability; circuit design; FPGA design.

DOI: 10.1504/IJMIC.2023.133430

International Journal of Modelling, Identification and Control, 2023 Vol.43 No.4, pp.267 - 283

Received: 12 Aug 2022
Received in revised form: 12 Sep 2022
Accepted: 05 Oct 2022
Published online: 15 Sep 2023 *

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