CANDYS/QA - A SOFTWARE SYSTEM FOR QUALITATIVE ANALYSIS OF NONLINEAR DYNAMICAL SYSTEMS

Numerical methods are often needed if bifurcation phenomena in nonlinear dynamical systems are studied. In this paper the software system CANDYS/QA for numerical qualitative analysis is presented. A wide class of problems is treated: computation of invariant sets (e.g., steady-states and periodic orbits), path-following (continuation) of such sets, and the related bifurcation phenomena. The following bifurcation situations are detected and the corresponding critical points are calculated during path-following: turning, bifurcation, Hopf bifurcation, period-doubling, torus bifurcation points (one-parameter problems) as well as cusp and Takens-Bogdanov points (two-parameter problems). A number of newly developed methods (e.g., for computation of the Poincare map) as well as algorithms from the literature are described to demonstrate the whole procedure of a qualitative analysis by numerical means. An illustrative example analyzed by CANDYS/QA is included.