Symmetry-recovering crises of chaos in polarization-related optical bistability

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Abstract
We investigate delay-induced chaos in an optically bistable system which has a symmetry with respect to the exchange of two circular polarizations. Roughly speaking, the output of the system bifurcates in the following way as the input light intensity increases: (1) symmetric steady state, (2) asymmetric steady state, (3) asymmetric periodic oscillation, (4) asymmetric chaos, and (5) symmetric chaos. The first bifurcation is a well-known symmetry-breaking transition. It is shown that the last bifurcation through which the symmetry is recovered can be viewed as a crisis of chaos, which has been defined by Grebogi et al. as a sudden change of strange attractor. By changing system parameters, we find three distinct types of the crises in the experiment with an electronic circuit which simulates the difference-differntial system equation. Before and after the crises, waveforms characteristic of each type are observed. In a simple two-dimensional-map model, we can find all three types of crises. It is also found that the types of crises are determined by the nature of unstable fixed (or periodic) points which cause the crises by colliding with the chaotic attractors. The symmetry-recovering crises seem to be general phenomena appearing in nonlinear systems with some symmetries.