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

Sherif H Elmeligy Abdelhamid,Henning S Mortveit,Chris J Kuhlman,Madhav V Marathe,S S Ravi,Ramesh Balasubramaniam

doi:10.1371/journal.pone.0133660

Sherif H Elmeligy Abdelhamid, Henning S Mortveit + Show 4 more

Open Access

https://doi.org/10.1371/journal.pone.0133660

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Abstract

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 state 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.

Highlights

Background and MotivationCivil disobedience [1], addiction [2], emotional behavior [3], social media [4], biology [5], and finance [6] are some of the research topics that are studied using agent-based modeling
We provide four example research problems solved with GDSC
The fourth study demonstrates the wider applicability of GDSC by illustrating how dynamical systems used by other researchers (e.g., [5]) can be modeled in this framework

Summary

Background and Motivation

Civil disobedience [1], addiction [2], emotional behavior [3], social media [4], biology [5], and finance [6] are some of the research topics that are studied using agent-based modeling. 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. ; fnðx1⁄2nÞÞ : We refer to this subclass of GDS as synchronous dynamics systems (SyDS), since all vertex functions are executed simultaneously (i.e., in parallel); it is sometimes referred to as generalized cellular automata In the latter case we consider permutation update sequences. For each of the sequential GDS and the block sequential GDS, there is one attractor and one basin of attraction; this means that all states eventually transition to the respective limit cycle No pair of these three GDSs are functionally equivalent because they do not produce the same state transitions; i.e., the same phase spaces.

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