Heteroclinic cycle

In mathematics, a heteroclinic cycle is an invariant set in the phase space of a dynamical system.

It is a topological circle of equilibrium points and connecting heteroclinic orbits.

In generic dynamical systems heteroclinic connections are of high co-dimension, that is, they will not persist if parameters are varied.

Robust cycles often arise in the presence of symmetry or other constraints which force the existence of invariant hyperplanes.

This cycle has also been studied in the context of rotating convection, and as three competing species in population dynamics.