In this paper, we discuss the dynamics of a discrete reduced Lorenz system. At first, applying the centre manifold reduction, computing normal form, using Takens's theorem and the equivalence between the mappings and the time 1 mappings of flows, we investigate the topological types of a fixed point for the system, including hyperbolic and non-hyperbolic. Then, we prove that the system undergoes the 1:2 resonance and 1:3 resonance and present all bifurcations as the parameters vary near the 1:2 resonance point and the 1:3 one, respectively. At last, by our results, we numerically simulate the scenes of bifurcations as the parameters vary near the 1:2 resonance point and the 1:3 resonance point, respectively. Furthermore, we show by numerical simulation that near the 1:3 resonance point the system possesses more plentiful dynamical properties, including invariant sets formed by three circles, 12-periodic cycles with four points on each circle, 3-coexisting chaotic attractors and full chaotic attractors.

在本文中，我们讨论离散约简洛伦兹系统的动力学。首先，应用中心流形约简，计算范式，利用Takens定理以及流的映射和时间1映射之间的等价性，我们研究了系统不动点的拓扑类型，包括双曲和非双曲。然后，我们证明系统经历了 1:2 共振和 1:3 共振，并且当参数分别在 1:2 共振点和 1:3 共振点附近变化时呈现所有分叉。最后，根据我们的结果，当参数分别在 1:2 共振点和 1:3 共振点附近变化时，我们数值模拟了分叉的场景。此外，我们通过数值模拟表明，在 1:3 共振点附近，系统具有更丰富的动力学特性，