FPGA Based Hardware Implementation of New Chaotic Hyperjerk System with Trigonometric Functions and, Multistability Analysis in Fractional Order Form

Ramar, Rameshbabu; Vaidhyanathan, Sundarapandian; Lujano-Hernandez, Luis C.; Munoz-Pacheco, Jesus M.

doi:10.24200/sci.2025.66424.10043

FPGA Based Hardware Implementation of New Chaotic Hyperjerk System with Trigonometric Functions and, Multistability Analysis in Fractional Order Form

Articles in Press

Document Type : Research Article

Authors

Rameshbabu Ramar ¹

Sundarapandian Vaidhyanathan ²

Luis C. Lujano-Hernandez ³

Jesus M. Munoz-Pacheco ⁴

¹ Department of Electronics and Communication Engineering, V.S.B. Engineering College, Karur, Tamilnadu 639111 – India

² Centre for Control Systems, Vel Tech University, Vel Nagar, Chennai-600 062, India

³ Faculty of Electronics Sciences, Benemerita Universidad Autonoma de Puebla, Av. San Claudio y 18 Sur, Puebla, 72570, Puebla, Mexico

⁴ Faculty of Electronics Sciences, Benemerita Universidad Autonoma de Puebla, Av. San Claudio y 18 Sur, Puebla, 72570, Puebla, Mexico.

10.24200/sci.2025.66424.10043

Abstract

This research article introduces a novel chaotic hyperjerk system incorporating two hyperbolic sinusoidal functions and explores its bifurcation analysis in both integer and fractional orders. The bifurcation analysis, Lyapunov spectrum analysis and phase portraits show that the proposed system exhibits wide range of complex phenomena such as chaos and multistability. The multistability phenomenon is analysed in detail with the fractional-order modelling, where the system’s fractional dynamics are captured using Garappa method. The development of fractional order chaotic system results in more complex dynamical response and the presence of hyperchaos over a broad range of system parameter. Additionally, the proposed integer order hyperjerk system is implemented on a DE10-Standard digital board, which comprises a Cyclone V SE 5CSXFC6D6F31C6N FPGA to realize its chaotic behaviour for various real-time applications. The results suggest that the proposed system could serve as a promising candidate in various domains where multistability and fractional-order systems are of interest.

Keywords

Chaos

Hyperjerk

Multistability

Fractional order

FPGA Implementation

Subjects