Period-1 to Period-4 Motions in a 5D Lorenz System

Abstract

In this paper, a 5D Lorenz system is discussed. The discrete mappings are developed to solve the periodic motions in the 5D Lorenz system. Then the stability and bifurcations are determined by eigenvalue analysis. A bifurcation tree is presented to demonstrate that the discrete mapping method can provide not only stable orbits but also unstable motions. Finally, trajectory illustrations are given to show bifurcation influences on periodic orbits and homoclinic orbits in the 5D Lorenz system.