 Heteroclinic cycle

A heteroclinic cycle is a closed chain of invariant states joined by heteroclinic orbits. For three equilibrium points $p_1,p_2,p_3$, the connections can run $p_1\to p_2\to p_3\to p_1$. The cycle consists of those connections and their limiting equilibria; it is not a single periodic orbit completing a circuit in finite time.

Nearby trajectories can spend long intervals close to one equilibrium before switching to the next. In convection-amplitude models this can describe successive convection roll switching. Whether trajectories remain near the chain depends on both local expansion and contraction rates and on the global connections. An invasion growth rate at one roll state alone does not establish an attracting cycle.

Invariant coordinate planes or other symmetries can preserve connections that an unrestricted perturbation would break. Consequently existence, robustness and attraction are separate questions.