This paper presents an effective approach to constructing numerical attractors of a general class of continuous homogenous dynamical systems: decomposing an attractor as a convex combination of a set of other existing attractors. For this purpose, the convergent Parameter Switching (PS) numerical method is used to integrate the underlying dynamical system. The method is built on a convergent fixed step-size numerical method for ODEs. The paper shows that the PS algorithm, incorporating two binary operations, can be used to approximate any numerical attractor via a convex combination of some existing attractors. Several examples are presented to show the effectiveness of the proposed method.

本文提出了一种有效的方法来构造一般类连续均质动力系统的数值吸引子：将吸引子分解为一组其他现有吸引子的凸组合。为此，使用收敛参数切换（PS）数值方法来集成基础动力学系统。该方法基于ODE的收敛固定步长数值方法。本文表明，结合了两个二进制运算的PS算法可通过一些现有吸引子的凸组合来近似任何数值吸引子。给出了几个例子来说明所提方法的有效性。