Social Balance and the Bernoulli Equation

Abstract

Since the 1940s there has been an interest in the question of why social networks often give rise to two antagonistic factions. Recently a dynamical model of how and why such a balance might occur was developed. This article provides an introduction to the notion of social balance and a new (and simplified) analysis of that model. This new analysis allows us to choose general initial conditions, as opposed to the symmetric ones previously considered. We show that for general initial conditions, four factions will evolve instead of two. We characterize the four factions, and give an idea of their relative sizes.

Keywords:

• MSC: Primary 37C10
• Secondary 91D30
• 05C90

Acknowledgment

I am grateful to Patrick de Leenheer for his insightful comments and indebted to Dacian Daescu for providing the software used to make figure displaying the simulation.

Additional information

Notes on contributors

J. J. P. Veerman

J. J. P. Veerman received his Ph.D. from Cornell University. He has held visiting positions in the U.S. (Rockefeller University, Georgia Tech, Penn State), as well as in Spain, Brazil, Italy, and Greece. He is currently at Portland State University in Oregon, USA, where he is Professor of Mathematics.

Maseeh Department of Mathematics and Statistics, Portland State University, Portland, OR 97201 [email protected]