On the boundaries of the parametric resonance domain (Q2761364)

The authors consider a system of linear homogeneous differential equations with periodic coefficients \(\dot x = Gx\), \(x\in \mathbb R^m\), \(G=G(t)\) is a real matrix of dimension \(m\times m\), continuous in \(t\) and periodic with period \(T\), \(G(t+T)=G(t)\). A method is proposed for estimating the domain of stability in a neighborhood of a boundary point (regular or singular) in the case of two and three parameters. As an example, the authors consider stability problem for an articulated pipe with fluid flowing with a pulsating velocity.