Delay-induced instabilities in nonlinear feedback systems

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Abstract
Extending general methods developed in synergetics to construct order-parameter equations we work out a systematic elimination procedure for the stable modes in nonlinear delay systems. It will be shown that in the vicinity of an instability the dynamical behavior of the infinite-dimensional delay system is approximately governed by a low-dimensional set of order-parameter equations which turn out to be of the form of ordinary differential equations, i.e., they no longer contain memory terms. The general formalism will then be compared with experimental data obtained from the nonlinear operation of a phase-locked loop where the finite propagation time of the signal in the feedback loop is taken into account.