Bio-inspired evolutionary dynamics on complex networks under uncertain cross-inhibitory signals

Given a large population of agents, each agent has three possiblechoices between option 1 or 2 or no option. The two options are equally favorable and the population has to reach consensus on one of the two options quickly and in a distributed way. The more popular an option is, the more likely it is to be chosen by uncommitted agents. Agents committed to one option can be attracted by those committed to the other option through a cross-inhibitory signal. This model originates in the context of honeybee swarms, and we generalize it to duopolistic competition and opinion dynamics. The contributions of this work include (i) the formulation of a model to explain the behavioral traits of the honeybees in the case where the interactions are modeled through complex networks, (ii) the study of the individual and collective behavior that leads to deadlock or consensus depending on a threshold for the cross-inhibitory parameter, (iii) the analysis of the impact of the connectivity on consensus, and (iv) the study of absolute stability for the collective system under time-varying and uncertain cross-inhibitory parameter.