We investigate the coexistence of low- and high-frequency oscillations in a delayed optoelectronic oscillator. We identify two nearby Hopf bifurcation points exhibiting low and high frequencies and demonstrate analytically how they lead to stable solutions. We then show numerically that these two branches of solutions undergo higher order instabilities as the feedback rate is increased but remain separated in the bifurcation diagram. The two bifurcation routes can be followed independently by either progressively increasing or decreasing the bifurcation parameter.
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