构造Lorenz系统周期解的数值分析方法
A Numerical-Analytical Method for Constructing Periodic Solutions of the Lorenz System
摘要：
本文给出了用系统参数的经典值构造动力学Lorenz系统周期解的一种近似方法。作者得到了一组关于谐波的循环频率、常数项和振幅的一般形式的非线性代数方程，它们构成了对所需解的谐波近似。选择牛顿法的初始近似，其收敛到描述不同于平衡位置的周期解的解。计算实验的结果。使用高精度计算验证了结果。
英文摘要：
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form concerning of the cyclic frequency, constant terms and amplitudes of harmonics that make up harmonic approximations to the desired solutions. The initial approximation for the Newton method is selected, which converges to a solution describing a periodic solution different from the equilibrium position. The results of a computational experiment are presented. The results are verified using high-precision calculations.
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