Comparing Dynamical Systems By Graph Matching Method

In this paper, we consider comparing dynamical systems by using graph matching method either between the graphs representing the underlying symbolic dynamics, or graphs approximating the action of the systems on a fine but otherwise non generating partition. For conjugate systems, the graphs are isomorphic and we show that the permutation matrices that relate the adjacency matrices coincides with the solution of Monge’s mass transport problem. We use the underlying Earth Mover’s Distance (EMD) to generate the “approximate” matching matrix to illustrate the association of graphs which are derived from equal-distance partitioning of the phase spaces of systems. In addition, for one system which embeds into the other, we show that the comparison of these two systems by our method is an issue of subgraph matching.