# Decomposition and Clustering for the Visualization of Dynamical Systems

## Abstract

We discuss recently developed methods for the visualization of dynamical systems which are based on the decomposition of the phase space of the system. The information of the system is represented by a directed graph and then the graph will be decomposed into smaller subsets which eventually defines a partition of the phase space. Depending on the purpose of visualization and the nature of the system, two different decompositions are introduced. The first decomposition algorithm is called Conley-Morse decomposition, which decompose the system according to the gradient-like structure of the system. On the other hand, the latter algorithm, an application of the peer pressure clustering algorithm for directed graphs, decompose each recurrent components of the system into further smaller non-invariant subsets according to the similarity of the dynamical behavior.

### Keywords

Dynamical systems Strongly connected components Conley-Morse decomposition Graph clustering Peer pressure clustering### References

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