An octave package to perform qualitative analysis of nonlinear systems immersed in R4

Eder Escobar; Richard Abramonte; Antenor Aliaga; Flabio Gutierrez

doi:10.3233/FAIA200775

An octave package to perform qualitative analysis of nonlinear systems immersed in R⁴

Eder Escobar, Richard Abramonte, Antenor Aliaga, Flabio Gutierrez

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

In this work, the AutonomousSystems4D package is presented, which allows the qualitative analysis of non-linear differential equation systems in four dimensions, as well as drawing the phase surfaces by immersing R4 in R3. The package is programmed in the computational tool Octave. As a case study applied to the new Lorenz 4D System, sensitivity was found in the initial conditions, Lyapunov exponents, Kaplan Yorke dimension, a stable and unstable critical point, limit cycle, Hopf bifurcation, and hyperattractors. The package could be adapted to perform qualitative analysis and visualize phase surfaces to autonomous systems, e.g. Sprott 4D, Rossler 4D, etc. The package can be applied to problems such as: design, analysis, implementation of electronic circuits; to message encryption.

Original language	English
Title of host publication	Machine Learning and Artificial Intelligence - Proceedings of MLIS 2020
Editors	Antonio J. Tallon-Ballesteros, Chi-Hua Chen
Publisher	IOS Press BV
Pages	136-145
Number of pages	10
ISBN (Electronic)	9781643681368
DOIs	https://doi.org/10.3233/FAIA200775
State	Published - 2 Dec 2020
Event	2020 International Conference on Machine Learning and Intelligent Systems, MLIS 2020 - Virtual, Online, Korea, Republic of Duration: 25 Oct 2020 → 28 Oct 2020

Publication series

Name	Frontiers in Artificial Intelligence and Applications
Volume	332
ISSN (Print)	0922-6389
ISSN (Electronic)	1879-8314

Conference

Conference	2020 International Conference on Machine Learning and Intelligent Systems, MLIS 2020
Country/Territory	Korea, Republic of
City	Virtual, Online
Period	25/10/20 → 28/10/20

Keywords

Autonomous System
Fourth dimension
Octave
Qualitative analysis

Access to Document

10.3233/FAIA200775

Cite this

Escobar, E., Abramonte, R., Aliaga, A., & Gutierrez, F. (2020). An octave package to perform qualitative analysis of nonlinear systems immersed in R⁴. In A. J. Tallon-Ballesteros, & C.-H. Chen (Eds.), Machine Learning and Artificial Intelligence - Proceedings of MLIS 2020 (pp. 136-145). (Frontiers in Artificial Intelligence and Applications; Vol. 332). IOS Press BV. https://doi.org/10.3233/FAIA200775

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abstract = "In this work, the AutonomousSystems4D package is presented, which allows the qualitative analysis of non-linear differential equation systems in four dimensions, as well as drawing the phase surfaces by immersing R4 in R3. The package is programmed in the computational tool Octave. As a case study applied to the new Lorenz 4D System, sensitivity was found in the initial conditions, Lyapunov exponents, Kaplan Yorke dimension, a stable and unstable critical point, limit cycle, Hopf bifurcation, and hyperattractors. The package could be adapted to perform qualitative analysis and visualize phase surfaces to autonomous systems, e.g. Sprott 4D, Rossler 4D, etc. The package can be applied to problems such as: design, analysis, implementation of electronic circuits; to message encryption.",

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Escobar, E , Abramonte, R , Aliaga, A & Gutierrez, F 2020, An octave package to perform qualitative analysis of nonlinear systems immersed in R⁴. in AJ Tallon-Ballesteros & C-H Chen (eds), Machine Learning and Artificial Intelligence - Proceedings of MLIS 2020. Frontiers in Artificial Intelligence and Applications, vol. 332, IOS Press BV, pp. 136-145, 2020 International Conference on Machine Learning and Intelligent Systems, MLIS 2020, Virtual, Online, Korea, Republic of, 25/10/20. https://doi.org/10.3233/FAIA200775

An octave package to perform qualitative analysis of nonlinear systems immersed in R⁴. / Escobar, Eder ; Abramonte, Richard ; Aliaga, Antenor et al.
Machine Learning and Artificial Intelligence - Proceedings of MLIS 2020. ed. / Antonio J. Tallon-Ballesteros; Chi-Hua Chen. IOS Press BV, 2020. p. 136-145 (Frontiers in Artificial Intelligence and Applications; Vol. 332).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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