GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems

Sherif H. Elmeligy Abdelhamid, Chris J. Kuhlman, Madhav V. Marathe, Henning S. Mortveit, S. S. Ravi, Ramesh Balasubramaniam
2015 PLoS ONE  
Discrete dynamical systems are used to model various realistic systems in network science, from social unrest in human populations to regulation in biological networks. A common approach is to model the agents of a system as vertices of a graph, and the pairwise interactions between agents as edges. Agents are in one of a finite set of states at each discrete time step and are assigned functions that describe how their states change based on neighborhood relations. Full characterization of
more » ... transitions of one system can give insights into fundamental behaviors of other dynamical systems. In this paper, we describe a discrete graph dynamical systems (GDSs) application called GDSCalc for computing and characterizing system dynamics. It is an open access system that is used through a web interface. We provide an overview of GDS theory. This theory is the basis of the web application; i.e., an understanding of GDS provides an understanding of the software features, while abstracting away implementation details. We present a set of illustrative examples to demonstrate its use in education and research. Finally, we compare GDSCalc with other discrete dynamical system software tools. Our perspective is that no single software tool will perform all computations that may be required by all users; tools typically have particular features that are more suitable for some tasks. We situate GDSCalc within this space of software tools. 2. Illustrative examples using GDSCalc. We provide four examples that highlight the usefulness of GDSC for classroom use and research. Although our focus here is on research, our examples will also bring out the usefulness of GDSC for educational purposes. (Terms used here are defined below.) These examples also address features of the system. The first example describes how GDSC was used to find a class of GDS, based on trees (acyclic graphs), that generate particular long-term dynamics: a user-specified limit cycle size. The second example addresses stability and evolution. It illustrates how GDSC was used to find classes of GDS that produce arbitrarily large limit cycles, and limit cycles that form undirected binary hypercubes in attractor graphs. Both of these results significantly extend the state-of-the-art on system GDSCalc PLOS ONE | In this section, we formally present the GDS. Then, to make the ideas concrete, we present two vertex functions for vertex state update, followed by examples of GDSs. Variants of the GDS formalism can be found in [17] . In the last subsection, we make a few comments about the GDSC software, relating it to the GDS model.
doi:10.1371/journal.pone.0133660 pmid:26263006 pmcid:PMC4532456 fatcat:mmb2vvvz5jc6fddkbecvjqoz4i