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

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

1 Cita (Scopus)

Resumen

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.

Idioma original	Inglés
Título de la publicación alojada	Machine Learning and Artificial Intelligence - Proceedings of MLIS 2020
Editores	Antonio J. Tallon-Ballesteros, Chi-Hua Chen
Editorial	IOS Press BV
Páginas	136-145
Número de páginas	10
ISBN (versión digital)	9781643681368
DOI	https://doi.org/10.3233/FAIA200775
Estado	Publicada - 2 dic. 2020
Evento	2020 International Conference on Machine Learning and Intelligent Systems, MLIS 2020 - Virtual, Online, República de Corea Duración: 25 oct. 2020 → 28 oct. 2020

Serie de la publicación

Nombre	Frontiers in Artificial Intelligence and Applications
Volumen	332
ISSN (versión impresa)	0922-6389
ISSN (versión digital)	1879-8314

Conferencia

Conferencia	2020 International Conference on Machine Learning and Intelligent Systems, MLIS 2020
País/Territorio	República de Corea
Ciudad	Virtual, Online
Período	25/10/20 → 28/10/20

Acceder al documento

10.3233/FAIA200775

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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. En 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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title = "An octave package to perform qualitative analysis of nonlinear systems immersed in R4",

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.",

keywords = "Autonomous System, Fourth dimension, Octave, Qualitative analysis",

author = "Eder Escobar and Richard Abramonte and Antenor Aliaga and Flabio Gutierrez",

note = "Publisher Copyright: {\textcopyright} 2020 The authors and IOS Press.; 2020 International Conference on Machine Learning and Intelligent Systems, MLIS 2020 ; Conference date: 25-10-2020 Through 28-10-2020",

year = "2020",

month = dec,

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doi = "10.3233/FAIA200775",

language = "English",

series = "Frontiers in Artificial Intelligence and Applications",

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booktitle = "Machine Learning and Artificial Intelligence - Proceedings of MLIS 2020",

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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. En 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, República de Corea, 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).

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

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AB - 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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