The periodic forcing of nonlinear oscillations can often be cast as a problem involving self-maps of the circle. Consideration of the effects of changes in the frequency and amplitude of the periodic forcing leads to a problem involving the bifurcations of circle maps in a two-dimensional parameter space. The global bifurcations in this two-dimensional parameter space is described for periodic ...

The choice of calibration policy is of basic importance in analytical chemistry. A prototype of the practical calibration problem is formulated as a mathematical task and a Bayesian solution of the resulting decision problem is presented. The optimum feedback calibration policy can then be found by dynamic programming. The underlying parameter estimation and filtering are solved by updating rel...