Analysis of the effects of time delay in nonlinear systems using generalised frequency response functions

A recursive algorithm for computing the generalised frequency response functions (GFRFs) of nonlinear time delay systems described by nonlinear differential-difference equation models is derived using the operator εnεn and used to analyse the effects of time delay in nonlinear systems. The algorithm shows an explicit relationship between the model parameters and the GFRFs. Such a relationship provides important insight into the behaviour of nonlinear systems. The effect of delay on several properties of nonlinear systems such as harmonic generation, gain compression/expansion and desensitisation is studied by considering the example of a Duffing oscillator with retarded damping. Results of the studies convincingly demonstrate that the system delay has a significant effect on several important properties of nonlinear systems.