关于分段线性Duffing型系统的一个注记
A note on a piecewise-linear Duffing-type system
摘要：
在最近的工作中，有人建议，在一个分段线性系的极限环的数量可以密切相关的区域的数量，即系统是线性的相平面的部分的数量。本文构造了一类具有n个区域的扰动分段系统的例子，使得位移函数的一阶变分恒为零。然后利用位移函数的二阶变分表示为连续函数，推测系统不存在极限环。这个系统在控制理论中可以看作是一个反馈系统。
英文摘要：
In a recent work it was suggested that the number of limit cycles in a piecewise-linear system could be closely related to the number of zones, that is the number of parts of the phase plane where the system is linear. In this note we construct an example of a class of perturbed piecewise systems with n zones such that the first variation of the displacement function is identically zero. Then we conjecture that the system has no limit cycles using the second variation of the displacement function expressed for continuous functions. This system can be seen as a feedback system in control theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
