Stable and unstable equilibria in the dynamic model of political competition between two parties

Document Type : Promotional Paper

Authors

1 Department of Pure Mathematics, Faculty of Mathematical Sciences, Yazd University, Yazd, Iran

2 Political Thought in Islam Group, Imam Khomeini and the Islamic Revolution Research Institute

Abstract

The inevitable conflict arising from the clash between two groups of different paradigms is a prominent phenomenon, and political competition for garnering the votes of citizens represents a prominent aspect of this conflict. In democratic societies, this confrontation reaches its peak before elections, ultimately leading to a relative equilibrium with the absolute or relative superiority of one of the parties. This article focuses on the dynamics of competition between two political parties and the process of reaching equilibrium, as well as the type of equilibrium in terms of stability. The degree of influence of each component of the parties' power in the emergence of the equilibrium point in party competition and the stability of the system around this point are issues that each party or group needs to address for its planning. The second issue is knowing, given the current situation, how to reach the equilibrium point in terms of the number of supporters of the two rival parties, and when is it possible? The pattern of models for infectious diseases and concepts of dynamic systems are used to model the process of changes in the number of supporters of the two rival political parties and study their competition dynamics. According to the results obtained, this system has one stable equilibrium point and three unstable equilibrium points. The initial conditions of both parties in any situation gradually move the system towards the stable equilibrium point. The timing of approaching this situation is also of great importance, which has been examined for several cases.

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References

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Mathematics and Society
Volume 5, Issue 4
December 2020
Pages 69-85

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History

  • Receive Date: 15 July 2021
  • Revise Date: 02 November 2021
  • Accept Date: 08 August 2021
  • Publish Date: 19 February 2021

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