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Strongly Nonlinear Oscillators Subject to Delay

A large class of strongly nonlinear conservative oscillators subject to a delayed feedback are modeled mathematically by second-order delay differential equations. Recent applications include the control of crane oscillations and lasers subject to optoelectronic feedback. We apply the method of averaging in the case of weak damping and weak feedback and determine the bifurcation diagram of the limit-cycle solutions. We find that the coexistence of a stable equilibrium with one or several stable periodic solutions is unavoidable if the delay is sufficiently large.