Toward a dynamics for power and control in society

This paper concerns the dynamical interactions between the macro structures of a society. From three axioms governing social interaction, a combined cooperative‐competitive model consisting of a nonlinear differential system of equations is introduced. Various social and political phenomena are interpreted through the parameters (also called strategies) of the model, including coalitions, alliances, and revolutions. For example, four distinct types of revolutions can be identified. Questions of existence, uniqueness, and asymptotic stability of equilibria are answered. A striking feature of the model is that, in the constant parameter case, stability is assured, thus illustrating that social power and control systems change only when external or internal changes on the system parameters are imposed. These results are applied to alliances and revolutions with a focus on changes in the equilibria as determined by changes in the system parameters.

Key words:

• Social power
• social control
• alliances
• mathematical model
• dynamical systems
• positive matrices

Notes

Research Supported in part by State of Texas ARP Grant No. 010366–183.