一类三维分段光滑系统的穿越极限环

Crossing limit cycles of a 3D piecewise-smooth system

本文研究了一类三维分段光滑系统的穿越极限环.由于相空间被一个超平面分成两个区域,因而系统呈现两个不同的向量场.此外,系统还具有two-fold点,且在该点处两个向量场都与该超平面相切.本文证明系统穿越极限环的最大个数是2,给出了存在一个和两个穿越极限环的充要条件,并确定其周期及在切换流形上的穿越位置.

In this paper we investigate the crossing limit cycles of a 3 D discontinuous piecewise-smooth system. In this system, the phase space is divided into two regions by a hypersurface and thus the system presents two different vector fields.Meanwhile, the system presents two-fold in which both vector fields are tangent to the hypersurface. We prove that the maximum number of crossing limit cycles is 2 and give necessary and sufficient conditions for one and two crossing limit cycles respectively. Furthermore, the crossing locations of the crossing limit cycles are determined as well as their periods.