Heteroclinic Orbit Cycle

Dynamical system cycling between saddle equilibria via heteroclinic connections

Parameters

Heteroclinic cycle: a closed chain of fixed points (saddles) connected by heteroclinic orbits — trajectories running from one equilibrium's unstable manifold to another's stable manifold.

Near the cycle, solutions slow exponentially as they approach each saddle, creating characteristic slow–fast dynamics. With small noise, the system can escape the cycle.

May–Leonard equations Symmetry: Z_N
Instability index: