Abstract
Instabilities in a nonlinear Fabry-Perot resonator and in an equivalent nonlinear ring resonator with two component cavities are studied. A competition between the time-delayed feedbacks causes a "frustration" in selecting an oscillation mode. The oscillation frequency jumps discontinuously and at random as the ratio of delay times is varied. A number-theoretic method has been successfully applied to elucidate the characteristics of oscillation.
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