The dual double scroll equation

This paper extends the Poincaré half-map technique, developed for the double scroll equation, in order to analyze the quite different dynamics of the dual double scroll equation. Two new uses of the Poincaré half-maps are presented: they are used to locate the boundaries between the return/transfer/escape regions and to detect a period-one limit cycle. The Poincaré half-map technique is also used to detect homoclinic and heteroclinic orbits and to locate the region in parameter space for which stable attracting sets exist.