Some remarks on Jacobi stability

Abstract

The notion of Jacobi stability for geodesics of a Riemannian or Finslerian manifold can be extended to arbitrary dynamical systems. This is the differential geometric theory of the variational equations for deviation of whole trajectories to nearby ones. We apply this theory to the Brusselator and Van der Pohl equations, and examine the relationship between the linear stability of steady-states and the stability of transient states. We interpret the Jacobi stability as the robustness of the dynamical system.