Differential flow instability in dynamical systems without an unstable (activator) subsystem

Abstract

A new kind of instability, induced by a uniform differential flow, is predicted. It affects dynamical systems of three or more variables that do not contain an unstable subsystem (activator). This is in contrast to the Turing instability and to the differential flow induced chemical instability which destabilize the homogeneous state of activator-inhibitor systems by releasing the inherent tendency of the activator to grow. A chemical example is given. Arguments are presented that interpret the mechanism of the instability as arising from a resonant excitation of a subsystem due to the differential flow.