Networked Bio-Inspired Evolutionary Dynamics on a Multi-Population

We consider a multi-population, represented by a network of groups of individuals. Every player of each group can choose between two options, and we study the problem of reaching consensus. The dynamics not only depend on the dynamics within the group, but they also depend on the topology of the network, so neighboring groups influence individuals as well. First, we develop a mathematical model of this networked bio-inspired evolutionary behavior and we study its steady-state. We look at the special case where the underlying network topology is a regular and unweighted graph and show that the steady-state is a consensus equilibrium. A sufficient condition for exponential stability is given. Finally, a related networked dynamical system with connections to the Bass model is studied and we conclude the paper with simulations.