Dutta, T.K., Prajapati, P. and Haloi, S. (2016) Supercritical and Subcritical Hopf Bifurcations in Non-Linear Maps. International Journal of Innovative Research in Technology & Science, 4, 14-20.

has been cited by the following article:

• 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.