Existence of Supercritical Hopf Bifurcation on a Type-Lorenz System  

作　　者：Evodio Muñoz-Aguirre Jorge Alvarez-Mena Pablo Emilio Calderón-Saavedra Josué Ramírez-Ortega Francisco Gabriel Hernández-Zamora Evodio Muñoz-Aguirre;Jorge Alvarez-Mena;Pablo Emilio Calderón-Saavedra;Josué Ramírez-Ortega;Francisco Gabriel Hernández-Zamora(Universidad Veracruzana, Xalapa, México;Universidad del Tolima, Ibagué, Colombia)

机构地区：[1]Universidad Veracruzana, Xalapa, México [2]Universidad del Tolima, Ibagué, Colombia

出　　处：《Journal of Applied Mathematics and Physics》2023年第3期780-789,共10页应用数学与应用物理（英文）

摘　　要：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.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.

关 键 词：Lorenz-Type System Subcritical Hopf Bifurcation Supercritical Hopf Bifurcation Hopf Theorem 

分 类 号：O17[理学—数学]