Bifurcation analysis and chaos in a discrete reduced Lorenz system

• The dynamical behaviors of a discrete Lorenz system are investigated.
• The stability conditions of the fixed points are analyzed.
• The normal form theorem is applied to investigate dynamics of the system.
• Numerical simulations are presented to verify the theoretical results.

In this paper, the discrete reduced Lorenz system is considered. The dynamical behavior of the system is investigated. The existence and stability of the fixed points of this system are derived. The conditions for existence of a pitchfork bifurcation, flip bifurcation and Neimark–Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. The complex dynamics, bifurcations and chaos are displayed by numerical simulations.