Graphical dynamical systems and their applications to bio-social systems

  • Abhijin Adiga
  • Chris J. Kuhlman
  • Madhav V. MaratheEmail author
  • Henning S. Mortveit
  • S. S. Ravi
  • Anil Vullikanti


In this review paper, we discuss graphical dynamical systems (GDSs) and their applications to biological and social systems (bio-social systems). Traditionally, differential equation-based models have been central in modeling bio-social systems. GDSs provide an alternate modeling framework. This framework explicitly represents individual components of the system and captures the interactions among them via a network. The purpose of this review is to enable modelers to obtain an understanding of this basic mathematical and computational framework so that it can be used to study specific bio-social applications. The work covers the range from computational theory to simulation-based analysis. We also provide some directions for future work.


Graphical dynamical systems Mathematical modeling Simulation science Complexity theory Biological and social systems 



We thank members of the Network Dynamics and Simulation Science Laboratory (NDSSL) for their comments and input. Specifically, we thank Chris Barrett, Christian Reidys, Daniel Rosenkrantz and Richard Stearns for their collaboration on several papers discussed in this article. We thank the computer systems administrators and managers at the Biocomplexity Institute of Virginia Tech for their help in this and many other works: Dominik Borkowski, William Miles Gentry, Jeremy Johnson, William Marmagas, Douglas McMaster, Kevin Shinpaugh and Robert Wills. This work has been partially supported by DTRA CNIMS (Contract HDTRA1-11-D-0016-0001), NSF BIG DATA Grant IIS-1633028, NSF DIBBS Grant ACI-1443054 and NSF EAGER Grant CMMI-1745207. The US Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon.


The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the US Government.


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Copyright information

© Indian Institute of Technology Madras 2018

Authors and Affiliations

  • Abhijin Adiga
    • 1
  • Chris J. Kuhlman
    • 1
  • Madhav V. Marathe
    • 1
    • 2
    Email author
  • Henning S. Mortveit
    • 1
  • S. S. Ravi
    • 1
    • 3
  • Anil Vullikanti
    • 1
    • 2
  1. 1.Biocomplexity Institute and InitiativeUniversity of VirginiaCharlottesvilleUSA
  2. 2.Computer Science DepartmentUniversity of VirginiaCharlottesvilleUSA
  3. 3.University at Albany – State University of New YorkAlbanyUSA

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