Limit Cycles Induced by Threshold Nonlinearity in Planar Piecewise Linear Systems of Node-Focus or Node-Center Type
Jiafu Wang, Su He, Lihong Huang
Abstract
In this paper, we investigate limit cycles induced by threshold nonlinearity of piecewise linear (PWL) differential systems, which are node-focus type or node-center type with the focus or the center being virtual or boundary. To get the number and stability of limit cycles, we adopt a new displacement function with a better configuration than usual. For a given parameter subregion, we exhibit the exact number or the minimum number of limit cycles. In particular, sufficient conditions are established ensuring that there are exactly two limit cycles. When the focus is boundary, we not only show that the maximum number is two, but also verify that the exact number is zero, one or two by varying parameter subregions. Finally, the exact number as well as the stability are obtained in different parameter regions for the PWL differential systems of node-center type.