Delay-Induced Periodic Behaviour in Competitive Populations

We study a model of binary decisions in a fully connected network of interacting agents. Individual decisions are determined by social influence, coming from direct interactions with neighbours, and a group level pressure that accounts for social environment. In a competitive environment, the interplay of these two aspects results in the presence of a persistent disordered phase where no majority is formed. We show how the introduction of a delay mechanism in the agent’s detection of the global average choice may drastically change this scenario, giving rise to a coordinated self sustained periodic behaviour.