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

Escobar E.; Gutierrez F.; Lujan E.; Ipanaque R.; Silva C.; Abanto L. · Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2023) · DOI: 10.1007/978-3-031-37126-4_36

Resumen

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.

Instituciones: Universidad Nacional de Piura