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has been cited by the following article:

• TITLE: Local Dynamics Analysis of a Four-Dimensional Hyperchaotic Lorenz System

  AUTHORS: Yu Ren, Liangqiang Zhou

  KEYWORDS: Hyperchaotic Lorenz System, Stability, Pitchfork Bifurcation, Hopf Bifurcation, Central Manifold

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.10, October 11, 2023

  ABSTRACT: The local dynamical behaviors of a four-dimensional hyperchaotic Lorenz system, including stability and bifurcations, are investigated in this paper by analytical and numerical methods. The equilibriums and their stability under different parameter conditions are analyzed by applying Routh-Hurwitz criterion. The results indicate that the system may exist one, three and five equilibrium points for different system parameters. Based on the central manifold theorem and normal form theorem, the pitchfork bifurcation and Hopf bifurcation are studied respectively. By using the Hopf bifurcation theorem and calculating the first Lyapunov coefficient, the Hopf bifurcation of this system is obtained as supercritical for certain parameters. Finally, the results of theoretical parts are verified by some numerical simulations.