具有Plykin型吸引子的非自治流系统
A non-autonomous flow system with Plykin type attractor
摘要：
一个非自治的流系统的Plykin型吸引子，可以作为一个基础，为阐述真正的系统和设备，展示结构稳定的混沌动力学。起点是一个二维球面上的地图，由四个阶段的连续几何明显的转换。计算表明，在一定的参数范围内，该映射存在一致双曲吸引子。它可以用赤平投影在平面上表示。考虑到结构稳定性，对模型进行了修正，得到了一组两个非自治的一阶光滑系数微分方程。从计算结果可以看出，它在庞加莱截面上具有Plykin型吸引子。
英文摘要：
A non-autonomous flow system is introduced with an attractor of Plykin type that may serve as a base for elaboration of real systems and devices demonstrating the structurally stable chaotic dynamics. The starting point is a map on a two-dimensional sphere, consisting of four stages of continuous geometrically evident transformations. The computations indicate that in a certain parameter range the map has a uniformly hyperbolic attractor. It may be represented on a plane by means of a stereographic projection. Accounting structural stability, a modification of the model is undertaken to obtain a set of two non-autonomous differential equations of the first order with smooth coefficients. As follows from computations, it has the Plykin type attractor in the Poincaré cross-section.
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