Bi-instability and the global role of unstable resonant orbits in a drivenlaser

Driven class-B lasers are devices which possess quadratic nonlinearities an d are known to exhibit chaotic behavior. We describe the onset of global he teroclinic connections which give rise to chaotic saddles. These form the p recursor topology which creates both localized homoclinic chaos, as well as global mixed-mode heteroclinic chaos. To locate the relevant periodic orbi ts creating the precursor topology, approximate maps are derived using matc hed asymptotic expansions and subharmonic Melnikov theory. Locating the rel evant unstable fixed points of the maps provides an organizing framework to understand the global dynamics and chaos exhibited by the laser. (C) 2000 Published by Elsevier Science B.V.