TY - GEN
T1 - Graphical Visualization of Phase Surface of the Sprott Type A System Immersed in 4D
AU - Escobar, Eder
AU - Gutierrez, Flabio
AU - Lujan, Edwar
AU - Ipanaque, Rolando
AU - Silva, Cesar
AU - Abanto, Lemin
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Chaotic system
KW - Geometric visualization
KW - Octave software
KW - Sprott type A hyper attractor
UR - http://www.scopus.com/inward/record.url?scp=85165052167&partnerID=8YFLogxK
U2 - 10.1007/978-3-031-37126-4_36
DO - 10.1007/978-3-031-37126-4_36
M3 - Conference contribution
AN - SCOPUS:85165052167
SN - 9783031371257
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 566
EP - 582
BT - Computational Science and Its Applications – ICCSA 2023 Workshops, Proceedings
A2 - Gervasi, Osvaldo
A2 - Murgante, Beniamino
A2 - Scorza, Francesco
A2 - Rocha, Ana Maria A. C.
A2 - Garau, Chiara
A2 - Karaca, Yeliz
A2 - Torre, Carmelo M.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 23rd International Conference on Computational Science and Its Applications, ICCSA 2023
Y2 - 3 July 2023 through 6 July 2023
ER -