Takens-Bogdanov bifurcation in a two-component nonlinear optical system with diffractive feedback |
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| Authors: | E. V. Degtiarev V. Wataghin |
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| Affiliation: | 1. International Laser Centre, Moscow State University , 119899, Moscow, Russia;2. L?Sen Inc. , Las Cruces, New Mexico, 88011, USA;3. Dipartimento di Fisica Teorica, Università di Torino, and Istituto Nazionale di Fisica Nucleare , Sezione di Torino via P. Giuria 1, 10125, Turin, Italy |
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| Abstract: | Abstract We analyse the conditions for stationary and oscillatory instabilities in a system consisting of two nonlinear Kerr-type elements. For the nonlinearities of the opposite sign, there is a degenerate point in the parameter space where both instabilities have equal thresholds and the same spatial frequency. In a vicinity of this point the dynamics are extremely sensitive to variation in control parameters, demonstrating a complex superposition of steady and time-periodic solutions. We relate this behaviour to the theory of the Taken-Bogdanov bifurcation. |
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