Coexistence of conservative and dissipative behavior in reversible dynamical systems

Abstract

Externally injected class-B lasers are shown to be approximately described by a reversible three-dimensional flow. For critical values of the external field such a model displays symmetry-breaking bifurcations, where the structure of space changes from conservative to dissipative either in a continuous or discontinuous manner. As a consequence, the coexistence of the two behaviors is observed in suitable parameter ranges. Symmetry breaking is shown to explain the onset of the very stable periodic solutions exhibited by the physical system. Such bifurcations are then studied in the simpler context of two-dimensional flows and recognized as degenerate codimension-2 phenomena. Generic normal forms are finally introduced which describe the local bifurcation unfolding.