The number and stability of limit cycles for planar piecewise linear systems of node-saddle type
The autors study limit cycles of the piecewise linear system \[ \dot{\mathbf{x}} =\begin{cases} \begin{pmatrix} T^+ & -1 \\ D^+& 0 \end{pmatrix} \mathbf{x} + \begin{pmatrix} -b\\ a^+ \end{pmatrix}, \quad x >0\\ \begin{pmatrix} T^- & -1 \\ D^- & 0 \end{pmatrix} \mathbf{x} + \begin{pmatrix} 0\\ a^-\end{pmatrix}, \quad x <0, \end{cases} \] where \((x,y)^t \in \mathbb{R}^2\). They find the parameter regions, where the system has one limit cycle, two limit cycles or does not have limit cycles. The stability of the limit cycles is investigated as well.
scientific article; zbMATH DE number 6957997
scientific article