Graphical Visualization of Phase Surface of the Sprott Type A System Immersed in 4D

Eder Escobar, Flabio Gutierrez, Edwar Lujan, Rolando Ipanaque, Cesar Silva, Lemin Abanto

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

When formulating a system of differential equations, the main objective is to determine their solutions, in addition to visualizing the phase surface to observe the behavior of the physical phenomenon. In this work an algorithm is developed to graph phase surfaces and perform qualitative analysis to a four-dimensional (4D) system. The algorithm is implemented in the scientific software Octave obtaining the program called SystemSprott4D, which is applied to the Sprott type A system in 4D to be able to graph, phase surfaces, limit cycle and trajectories of initial conditions of the system. A qualitative analysis of the system is performed, such as symmetry of the vector field, sensitivity in the initial conditions, Lyapunov exponents, fractal dimension and limit cycle. It is found that it is a non-equilibrium system, this means that the 4D chaotic system can exhibit attracting limit cycles, these limit cycles are found by selecting different initial points. The program can be used to analyze non-linear 4D systems from various disciplines such as electronics, telecommunications, biology, meteorology, economics, medicine, etc.

Original languageEnglish
Title of host publicationComputational Science and Its Applications – ICCSA 2023 Workshops, Proceedings
EditorsOsvaldo Gervasi, Beniamino Murgante, Francesco Scorza, Ana Maria A. C. Rocha, Chiara Garau, Yeliz Karaca, Carmelo M. Torre
PublisherSpringer Science and Business Media Deutschland GmbH
Pages566-582
Number of pages17
ISBN (Print)9783031371257
DOIs
StatePublished - 2023
Event23rd International Conference on Computational Science and Its Applications, ICCSA 2023 - Athens, Greece
Duration: 3 Jul 20236 Jul 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14111 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference23rd International Conference on Computational Science and Its Applications, ICCSA 2023
Country/TerritoryGreece
CityAthens
Period3/07/236/07/23

Keywords

  • Chaotic system
  • Geometric visualization
  • Octave software
  • Sprott type A hyper attractor

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