Author(s)

Evodio Muñoz-Aguirre¹, Jorge Alvarez-Mena¹, Pablo Emilio Calderón-Saavedra², Josué Ramírez-Ortega¹, Francisco Gabriel Hernández-Zamora¹

¹Universidad Veracruzana, Xalapa, México.
²Universidad del Tolima, Ibagué, Colombia.

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.

Lorenz-Type System, Subcritical Hopf Bifurcation, Supercritical Hopf Bifurcation, Hopf Theorem

Muñoz-Aguirre, E. , Alvarez-Mena, J. , Calderón-Saavedra, P. , Ramírez-Ortega, J. and Hernández-Zamora, F. (2023) Existence of Supercritical Hopf Bifurcation on a Type-Lorenz System. Journal of Applied Mathematics and Physics, 11, 780-789. doi: 10.4236/jamp.2023.113052.