On the Effect of Collaborative and Antagonistic Interactions on Synchronization and Consensus in Networks of Conspecific Agents

While the vast majority of work on consensus and synchronization considers only collaborative interactions among the agents, antagonistic interactions may play important roles in coordination of social systems. In this work, we define a composite model over a stochastically-switching network capturing both collaborative and antagonistic interactions. We consider a general class of agents, so-called conspecifics, defined in terms of a common distribution for their interaction capacity and the weights they ascribe to interactions. We find closed form expressions for necessary and sufficient conditions for consensus, the rate of convergence to consensus, and conditions for stochastic synchronization. This model is further extended to composite topologies capable of capturing any number of independent interaction modes. Results demonstrate the presence of antagonistic interactions may help the system to achieve consensus and synchronization which is not possible in presence of only collaborative interactions and, at times, enables convergence at a faster rate.