Experimental Observation of Chaotic Attractors from the FPGA implementation of 3D Chaotic Systems

Abstract

AbstractIn recent years, researchers have designed and implemented chaotic oscillators using digital hardware elements to develop applications like secure communications and random number generation. Due to its programmability and low-cost characteristics, one of the most used digital devices to synthesize chaotic systems is the field-programmable gate array (FPGA), which is recommended for fast prototyping. In this manner, this paper shows the experimental observation of seven chaotic attractors that are simulated using the Verilog hardware description language, and implemented in an FPGA. The seven designs are Lorenz-type systems, which are designed from the discretization of their equations using the well-known Forward Euler method. The block description of the seven chaotic systems employs the fixed-point numerical format using 32 bit. The simulations of the chaotic systems using Matlab and Active-HDL software, along with the block diagrams of the designs, are presented. The final part of the work illustrates the experimental attractors on a Teledyne Lecroy oscilloscope, obtained by using an FPGA Cyclone II EP2C35F672C6 and a 16-bit digital-to-analog converter.KEYWORDS: Chaotic oscillatorChaosOne-step methodFPGAFixed-point format AcknowledgementsJ.D. Rodríguez-Muñoz thanks to CONAHCYT at México for the scholarship for pursuing a Master Degree at INAOE. J.D. Tavizón-Aldama thanks to Programa Delfín at México for the scholarship to pursue an internship at INAOE during the summer of 2023.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationNotes on contributorsJosé David Rodríguez-MuñozJosé David Rodríguez-Muñoz received the BSc degree in electronics engineering from the Tecnológico de Nuevo Laredo, Mexico, in 2021. He is currently pursuing an MSc degree in electronics with the Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Mexico. His research interests include chaotic systems, digital signal processing, and digital systems design with FPGA. Email: david.rodriguez@inaoe.mxJonathan Daniel Tavizón-AldamaJonathan Daniel Tavizón-Aldama is currently pursuing the BSc degree in electronics and communications engineering with the Centro Universitario de Ciencias Exactas e Ingeniería (CUCEI), Universidad de Guadalajara, Mexico. His research interest includes chaotic systems, embedded software, and digital signal processing. Email: jonathan.tavizon0028@alumnos.udg.mxEsteban Tlelo-CuautleEsteban Tlelo-Cuautle received the BSc degree from Instituto Tecnológico de Puebla, Mexico, in 1993, and the MSc and PhD degrees from Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Mexico, in 1995 and 2000, respectively. In 2001, he was appointed as a Professor-Researcher at INAOE. He has authored five books, edited 13 books, and around 300 works published in book chapters, inter- national journals, and conferences. His research interests include analog signal processing, synthesis and design of integrated circuits, optimization by metaheuristics, fractional chaotic systems, security in the internet of things, symbolic analysis, and analog/RF and mixed-signal design automation tools. He serves as associate editor for Engineering Applications of Artificial Intelligence, International Journal of Circuit Theory and Applications, Electronics, Integration the VLSI Journal, and Fractal and fractional. Corresponding author. Email: etlelo@inaoep.mx