A global qualitative view of bifurcations and dynamics in the Rössler system

The aim of the Letter is a global study of the well-known Rössler system to point out the main complex dynamics that it can exhibit. The structural analysis is based on the periodic solutions of the system investigated by a harmonic balance technique. Simplified expressions of such limit cycles are first derived and characterized, then their local bifurcations are denoted, also giving indications to predict possible homoclinic orbits with the same unifying approach. These analytical results give a general picture of the system behaviours in the parameter space and numerical analysis and simulations confirm the qualitative accuracy of the whole. Such predictions have also an important role in applying efficiently the above numerical procedures.