Generation of self-similarity in a chaotic system of attractors with many scrolls and their circuit’s implementation

A. Dlamini and E.F. Doungmo Goufo

Chaos, Solitons & Fractals, 2023, vol. 176, issue C

Abstract: The concept of self-similarity, widely employed in specialized fields of applied sciences, has been investigated through numerous works utilizing both analytical elements and experimental observations. As a significant component of both fractal and chaos theories, self-similarity can naturally manifest around us or be artificially simulated using mathematical arguments and algorithms. In this paper, we utilize analytical, numerical, and experimental circuit elements to study, analyze, and simulate a generalized chaotic system of attractors with multiple scrolls. This system presents various types of processes, including chaotic and hyperchaotic dynamics, as well as hidden attractors. We discuss the well-posedness of the system before examining its numerical solvability, error tolerance, and simulations for the model involving fractal and fractional operations. Simulations are conducted for various values of the model’s parameters, demonstrating that the system displays fractal features combined with chaotic behavior. The system is implemented using a Field Programmable Gate Array (FPGA) board, generating self-similar results akin to those obtained numerically.

Keywords: Self-similarity; Field programmable gate array (FPGA) board; Hidden attractors; Coexisting attractors (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923009852

DOI: 10.1016/j.chaos.2023.114084

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