Effects of Time-Dependent-Pararameter Variation on the Period-Doubling Route to Chaos.

A common method for investigating bifurcation points in physical systems consists in slowly changing a control parameter and observing the state of the system as a function of the instantaneous value of the parameter. The main reason for adopting this procedure is it’s convenience: An entire bifurcation diagram can be constructed in a single sweep of the bifurcation parameter. The literature on laser instabilities contains many examples of such studies.1