A Mechanism for Chaos in a Nonlinear Optical System
We show, using a global phase space analysis, that the chaotic attractor appearing beyond the accumulation point of period doubling bifurcations in a ring bistable cavity is the accumulation of homoclinic orbits associated with unstable fixed points which remain on each successive bifurcation. In contrast to the one dimensional map, periodic cycles of any arbitrary period may, in principle, appear abruptly in the phase space and these in turn can undergo period doubling.
KeywordsUnstable Manifold Chaotic Attractor Homoclinic Orbit Stable Manifold Period Doubling
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