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 ε n 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.