next up previous contents
Next: Stream arrows Up: Notes on the local Previous: System analysis near trajectories


Discussion

This chapter compiles important terms and definitions that are useful for analyzing analytically defined dynamical systems. Widely varying terms and denotations are sometimes used in literature to describe important concepts of dynamical systems. Thus a clarifying survey of these sometimes interchangeable terms and definitions is given.

After presenting a classification of dynamical systems, tools of differential geometry are discussed with respect to the analysis of trajectories of dynamical systems. The description of terms defining flow characteristics of dynamical systems (e.g., divergence, rotation) is followed by discussing linearization techniques for dynamical systems.

Together with an investigation of flow behavior close to a critical point and cycles a concept for the local analysis of a dynamical system close to an arbitrary trajectory is presented. This approach basically investigates perturbations orthogonal to the chosen trajectory by determining eigenvalues and eigenvectors of a matrix which is closely related to the Jacobian matrix of the dynamical system but with lower dimension.



Helwig Löffelmann, November 1998,
mailto:helwig@cg.tuwien.ac.at.