A shift down of the resonance frequency is claimed to be used as a simple practical test for the onset of chaos based on a common feature of forced damped nonlinear oscillation systems which exhibit cascading bifurcations to chaos.

An analytical method is developed to determine the critical value of the control parameter of a dynamical system above which chaos is initiated. An initial value problem for a dynamical system is shown to be solved with the aid of a continued fraction expansion which converges very rapidly. The result is confirmed by numerical experiments.