Stable orbits embedded in a chaotic attractor for a trapped ion interacting with a laser field

The interaction between a trapped ion and a resonant laser standing wave is studied under the analytical approximation. Periodic orbits next to the heteroclinic one and their stability conditions are derived from the Rayleigh perturbation method. Theoretical analysis reveals the stable periodic orbits to be embedded in the Melnikov chaotic attractor. The corresponding numerical results show that fitting control parameters into the stability conditions can control chaos in the system.