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中文摘要：
应用欧拉差分方法,构造了一个新的三维离散类Lorenz系统.讨论了该三维离散动力系统的动力学性质,分析了其不动点的存在性和稳定性.基于Neimark-Sacker分岔准则、中心流形定理和范式理论,研究了该系统Neimark-Sacker分岔的存在性、稳定性和方向.最后,通过数值仿真证明理论分析的正确性.
英文摘要：
A new three-dimensional discrete Lorenz-like system is proposed by using forward Euler scheme. The dynamics of this three-dimensional discrete Lorenz-like system is considered, and the existence and stability of equilibrium are also discussed. Based on explicit Neimark-Sacker bifurcation criterion, center manifold theory and normal form method, the system＇s existence, stability and direction of Neimark-Sacker bifurcation are studied. Finally, a numerical example is provided for justifying the valid- ity of the theoretical analysis.
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