TITLE:
Existence of Supercritical Hopf Bifurcation on a Type-Lorenz System
AUTHORS:
Evodio Muñoz-Aguirre, Jorge Alvarez-Mena, Pablo Emilio Calderón-Saavedra, Josué Ramírez-Ortega, Francisco Gabriel Hernández-Zamora
KEYWORDS:
Lorenz-Type System, Subcritical Hopf Bifurcation, Supercritical Hopf Bifurcation, Hopf Theorem
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.3,
March
28,
2023
ABSTRACT: In this paper, a system of Lorenz-type ordinary differential equations is considered and, under some assumptions about the parameter space, the presence of the supercritical non-degenerate Hopf bifurcation is demonstrated. The technical tool used consists of the Central Manifold theorem, a well-known formula to calculate the Lyapunov coefficient and Hopf’s Theorem. For particular values of the parameters in the parameter space established in the main result of this work, a graph is presented that describes the evolution of the trajectories, obtained by means of numerical simulation.