Chaotic Dynamics Analysis and FPGA Implementation Based on Gauss Legendre Integral

Li Wen, Li Cui (), Hairong Lin and Fei Yu ()
Additional contact information
Li Wen: School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
Li Cui: School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan 411201, China
Hairong Lin: School of Electronic Information, Central South University, Changsha 410083, China
Fei Yu: School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China

Mathematics, 2025, vol. 13, issue 2, 1-23

Abstract: In this paper, we first design the corresponding integration algorithm and matlab program according to the Gauss–Legendre integration principle. Then, we select the Lorenz system, the Duffing system, the hidden attractor chaotic system and the Multi-wing hidden chaotic attractor system for chaotic dynamics analysis. We apply the Gauss–Legendre integral and the Runge–Kutta algorithm to the solution of dissipative chaotic systems for the first time and analyze and compare the differences between the two algorithms. Then, we propose for the first time a chaotic basin of the attraction estimation method based on the Gauss–Legendre integral and Lyapunov exponent and the decision criterion of this method. This method can better obtain the region of chaotic basin of attraction and can better distinguish the attractor and pseudo-attractor, which provides a new way for chaotic system analysis. Finally, we use FPGA technology to realize four corresponding chaotic systems based on the Gauss–Legendre integration algorithm.

Keywords: Gauss–Legendre integral; basin of attraction; hidden attractor chaotic system; FPGA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/2/201/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/2/201/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:2:p:201-:d:1563614

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().