Synthesizing a return map

Since the mean field curve does not always follow the empirical data, provision has been made to generate an empirical curve, by prescribing the coefficients of a Bernstein polynomial. Cursor arrows or mouse movements are used to select the coefficient or to establish its value.

Provision has been made for a modifier, inspired by the idea of a probabilistic automaton, which can multiply each Bernstein monomial. The default values are all 1.0.

Another service which has been provided is to fit a parabola to a portion of the return map, the intention being to see how closely the dynamics of the classical logistic function can be matched. These options are very specific to the Chaté-Manneville automata, and must be used cautiously; otherwise floating point overflow is likely to occur. Some control over the points may be obtained by generating an initial field of known probability.

The option # requires that the coordinates of the points be stated explicitly.

Harold V. McIntosh