DELAY-INDUCED INSTABILITIES IN NONLINEAR FEEDBACK-SYSTEMS

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-dimension al set of order-parameter equations which turn out to be of the form o f 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 wher e the finite propagation time of the signal in the feedback loop is ta ken into account.