Issues on Applying One- and Multi-Step Numerical Methods to Chaotic Oscillators for FPGA Implementation

Omar Guillén-Fernández, María Fernanda Moreno-López and Esteban Tlelo-Cuautle
Additional contact information
Omar Guillén-Fernández: Department of Electronics, INAOE, Tonantintla, Puebla 72840, Mexico
María Fernanda Moreno-López: Department of Electronics, INAOE, Tonantintla, Puebla 72840, Mexico
Esteban Tlelo-Cuautle: Department of Electronics, INAOE, Tonantintla, Puebla 72840, Mexico

Mathematics, 2021, vol. 9, issue 2, 1-14

Abstract: Chaotic oscillators have been designed with embedded systems like field-programmable gate arrays (FPGAs), and applied in different engineering areas. However, the majority of works do not detail the issues when choosing a numerical method and the associated electronic implementation. In this manner, we show the FPGA implementation of chaotic and hyper-chaotic oscillators from the selection of a one-step or multi-step numerical method. We highlight that one challenge is the selection of the time-step h to increase the frequency of operation. The case studies include the application of three one-step and three multi-step numerical methods to simulate three chaotic and two hyper-chaotic oscillators. The numerical methods provide similar chaotic time-series, which are used within a time-series analyzer (TISEAN) to evaluate the Lyapunov exponents and Kaplan–Yorke dimension ( D K Y ) of the (hyper-)chaotic oscillators. The oscillators providing higher exponents and D K Y are chosen because higher values mean that the chaotic time series may be more random to find applications in chaotic secure communications. In addition, we choose representative numerical methods to perform their FPGA implementation, which hardware resources are described and counted. It is highlighted that the Forward Euler method requires the lowest hardware resources, but it has lower stability and exactness compared to other one-step and multi-step methods.

Keywords: chaotic oscillator; one-step method; multi-step method; computer arithmetic; FPGA (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/2/151/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/2/151/ (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:9:y:2021:i:2:p:151-:d:478846

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 ().