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

## 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 work, 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 thatmore »

- Authors:

- Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States). Computer Science Dept.
- Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States). Virginia Bioinformatics Inst.
- State Univ. of New York (SUNY), Albany, NY (United States). Computer Science Dept.

- Publication Date:

- Research Org.:
- Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC); USDOD Defense Threat Reduction Agency (DTRA); National Institutes of Health (NIH); National Science Foundation (NSF)

- OSTI Identifier:
- 1458519

- Grant/Contract Number:
- SC0003957; HDTRA1-11-1-0016; HDTRA1-11-D-0016-0001; 5U01GM070694-11; CNS-1011769; OCI-1032677

- Resource Type:
- Accepted Manuscript

- Journal Name:
- PLoS ONE

- Additional Journal Information:
- Journal Volume: 10; Journal Issue: 8; Journal ID: ISSN 1932-6203

- Publisher:
- Public Library of Science

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; dynamical systems; permutation; software tools; computer software; ergodicity; behavior; web-based applications; agent-based modeling

### Citation Formats

```
Elmeligy Abdelhamid, Sherif H., Kuhlman, Chris J., Marathe, Madhav V., Mortveit, Henning S., and Ravi, S. S. GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems. United States: N. p., 2015.
Web. doi:10.1371/journal.pone.0133660.
```

```
Elmeligy Abdelhamid, Sherif H., Kuhlman, Chris J., Marathe, Madhav V., Mortveit, Henning S., & Ravi, S. S. GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems. United States. doi:10.1371/journal.pone.0133660.
```

```
Elmeligy Abdelhamid, Sherif H., Kuhlman, Chris J., Marathe, Madhav V., Mortveit, Henning S., and Ravi, S. S. Tue .
"GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems". United States. doi:10.1371/journal.pone.0133660. https://www.osti.gov/servlets/purl/1458519.
```

```
@article{osti_1458519,
```

title = {GDSCalc: A Web-Based Application for Evaluating Discrete Graph Dynamical Systems},

author = {Elmeligy Abdelhamid, Sherif H. and Kuhlman, Chris J. and Marathe, Madhav V. and Mortveit, Henning S. and Ravi, S. S.},

abstractNote = {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 work, 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.},

doi = {10.1371/journal.pone.0133660},

journal = {PLoS ONE},

number = 8,

volume = 10,

place = {United States},

year = {2015},

month = {8}

}

Works referenced in this record:

##
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journal, May 2010

- Stone, John E.; Gohara, David; Shi, Guochun
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