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Dynamics of two-actor cooperation–competition conflict models

Author

Listed:
  • Liebovitch, Larry S.
  • Naudot, Vincent
  • Vallacher, Robin
  • Nowak, Andrzej
  • Bui-Wrzosinska, Lan
  • Coleman, Peter

Abstract

We present a nonlinear ordinary differential equation model of the conflict between two actors, who could be individuals, groups, or nations. The state of each actor depends on its own state in isolation, its previous state in time, its inertia to change, and the positive feedback (cooperation) or negative feedback (competition) from the other actor. We analytically determined the stability of the critical points of the model and explored its dynamical behavior through numerical integrations and analytical proofs. Some results of the model are consistent with previously observed characteristics of conflicts, and other results make new testable predictions on how the dynamics of a conflict and its outcome depend on the strategies chosen by the actors.

Suggested Citation

  • Liebovitch, Larry S. & Naudot, Vincent & Vallacher, Robin & Nowak, Andrzej & Bui-Wrzosinska, Lan & Coleman, Peter, 2008. "Dynamics of two-actor cooperation–competition conflict models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(25), pages 6360-6378.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:25:p:6360-6378
    DOI: 10.1016/j.physa.2008.07.020
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    Cited by:

    1. Flores, J.C. & Bologna, Mauro, 2013. "Troy: A simple nonlinear mathematical perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4683-4687.
    2. Iván Y Fernández-Rosales & Larry S Liebovitch & Lev Guzmán-Vargas, 2015. "The Dynamic Consequences of Cooperation and Competition in Small-World Networks," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-13, April.
    3. Kaufman, Miron & Diep, Hung T. & Kaufman, Sanda, 2019. "Sociophysics of intractable conflicts: Three-group dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 175-187.
    4. Ekaterina V. Orlova, 2024. "A Novel Brillouin and Langevin Functions Dynamic Model for Two Conflicting Social Groups: Study of R&D Processes," Mathematics, MDPI, vol. 12(17), pages 1-26, September.

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