Two species coagulation approach to consensus by group level interactions

Abstract

We explore the self-organization dynamics of a set of entities by considering the interactions that affect the different subgroups conforming the whole. To this end, we employ the widespread example of coagulation kinetics, and characterize which interaction types lead to consensus formation and which do not, as well as the corresponding different macroscopic patterns. The crucial technical point is extending the usual one species coagulation dynamics to the two species one. This is achieved by means of introducing explicitly solvable kernels which have a clear physical meaning. The corresponding solutions are calculated in the long time limit, in which consensus may or may not be reached. The lack of consensus is characterized by means of scaling limits of the solutions. The possible applications of our results to some topics in which consensus reaching is fundamental, like collective animal motion and opinion spreading dynamics, are also outlined.

References in corpus (8)

• Statistical physics of social dynamics
• Non-equilibrium clustering of self-propelled rods
• Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates
• Langevin description of critical phenomena with two symmetric absorbing states
• Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior
• Phase ordering with a global conservation law: Ostwald ripening and coalescence
• Noisy continuous--opinion dynamics
• On the Geometric Principles of Surface Growth

Cited by in corpus (3)

• Cluster dynamics and cluster size distributions in systems of self-propelled particles
• Ground states of a two phase model with cross and self attractive interactions
• Nonlinear degenerate cross-diffusion systems with nonlocal interaction