A global attractor consisting of exponentially unstable equilibria

Abstract

There exist examples in the literature of attractors consisting solely of unstable equilibria, but in these examples, the unstable equilibria are not exponentially unstable (the differentials of the vector fields at the unstable equilibria have no eigenvalues in the open right-half complex plane). In this paper we provide an example of a system having a compact global attractor consisting solely of exponentially unstable equilibria.