Stability of ordered equilibria

In this article we give an elementary method to investigate linear stability of equilibria of finite dimensional dynamical systems. In particular, under general hypotheses, the equilibria can be organised in an ordered chain along which the determinant of the associated Jacobian matrix has alternating sign. We develop the idea in two and three-dimensional cases, and then give a result for general n-dimensional systems. We also apply the technique to some particular, well known dynamical systems.