We present two large families of Shilnikov-type homoclinic orbits in a two mode-model that describes second-harmonic generation in a passive optical cavity. These families of homoclinic orbits give rise to chaotic dynamics in the model.

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This work was partly supported by the U.S. Department of Energy through grant DE-FG02-93ER25154, the National Science Foundation through grants DMS-9403750, DMS-9502142, and DMS-9510728, and the Alfred P. Sloan Foundation through a Sloan Research Fellowship.

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