Two-parameter bifurcation analysis of the discrete Lorenz model

This paper studies the bifurcation analysis of the discrete time Lorenz system considering its generalization for two control parameters. The one- and two-parameter bifurcations of the system, including pitchfork, period-doubling, Neimark–Sacker, 1:2, 1:3, and 1:4 resonances, are surveyed thoroughly. The critical coefficients are computed to analyze the nondegeneracy of listed bifurcations and predict their bifurcation scenarios. The numerical continuation method reveals complex dynamics including bifurcations up to 16th iterations. The results show an excellent agreement between the analytical predictions and the numerical observations.