Narrow-Band Excitation of a Nonlinear Oscillator

A nonlinear oscillator characterized by a hardening-type restoring force is excited by stationary narrow-band noise. The analysis is based on the concept of quasi-static amplitude and phase values which is exactly opposite to the stochastic or Markov approach with its associated Fokker-Planck equation. The approach, in effect, replaces a system with memory with one without memory. The existence of jumps is demonstrated and an expression for the probability of the occurrence of jumps is derived.