The qualitative analysis of a class of planar Filippov systems (Q984097)

Consider the system \[ \dot{x}= f(x), \] where \(x=(x_{1},x_{2})^{t}\), \(c=(c_{1},c_{2})^{t}\in\mathbb{R}^{2} \) and \[ f(x)=\begin{cases} A_{+}x +c,&\text{if \(x_{1}>0\)},\\ A_{-}x -c,&\text{if \(x_{1}<0\)},\end{cases}\qquad A_{+}=\begin{pmatrix} 0&1\\ a&b \end{pmatrix},\qquad A_{-}=\begin{pmatrix} 0&1\\ A&B \end{pmatrix}. \] Here \(a,A,b,B,c_{1},c_{2}\) are parameters, \(a,A>0.\) For \(|((b+B)c_{1}+2c_{2})/(b-B)|> c_{1}\), a complete qualitative analysis is provided including the existence and uniqueness of the initial value problem and the existence and uniqueness of a stationary point.