TAKENS-BOGDANOV BIFURCATION IN A 2-COMPONENT NONLINEAR-OPTICAL SYSTEMWITH DIFFRACTIVE FEEDBACK

We analyse the conditions for stationary and oscillatory instabilities in a system consisting of two nonlinear Kerr-type elements. For the n onlinearities of the opposite sign, there is a degenerate point in the parameter space where both instabilities have equal thresholds and th e 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 rel ate this behaviour to the theory of the Takens-Bogdanov bifurcation.