Abstract: The stabilization of an unstable periodic orbit in a neighborhood of an unstable fixed point is studied. By adding the external control signal, the straight-line stabilization method is applied to a high-dimensional Hamiltonian system, that is,two coupled standard maps. The method can stabilize an unstable periodic orbit in a neighborhood of an unstable fixed point, so the difficult problem of the unstable periodic orbits for high-dimensional Hamiltonian systems can be solved. The method does not require any previous knowledge of the system and is robust under the presence of weak external noise.

Key words: controlling chaos, straight-line stabilization method, two coupled standard maps