Characterization of the Rossler System in Parameter Space

We characterize the Rössler system by means of a map associating colors to various intervals of largest Lyapunov exponent values in parameter space. This color map allows quick access to quantitative information about the dynamics of the system. The map also permits parameter space navigation while intentionally maintaining the system in a desired state, and avoiding regions where the system's behavior would be undesirable. In addition, the map exhibits a rich structure of stability clusters composed of affine-similar repetitions of basic elementary cells called "swallows." These cells, until recently, have been known to be associated with discrete maps only.