Miles’ equation models the amplitude modulation of a Faraday wave. A dynamical system study is conducted on this concrete physical model. It turns out that a quartet of heteroclinic orbits can be located, but we fail to locate any homoclinic orbit. For a generalized Miles’ equation, a quartet of homoclinic orbits can be located, and existence of chaos can be proved under certain generic assumptions. 2004 Elsevier Ltd. All rights reserved.