Singularities of invariant densities for random switching between two linear ODEs in 2D (2009.01299v1)

Abstract: We consider a planar dynamical system generated by two stable linear vector fields with distinct fixed points and random switching between them. We characterize singularities of the invariant density in terms of the switching rates and contraction rates. We prove boundedness away from those singularities. We also discuss some motivating biological examples.