Unanimity Rule on Networks

We introduce a model for innovation-, evolution- and opinion dynamics whose spreading is dictated by unanimity rules, i.e., a node will change its (binary) state only if all of its neighbors have the same corresponding state. It is shown that a transition takes place depending on the initial condition of the problem. In particular, a critical number of initially activated nodes is needed so that the whole system gets activated in the long-time limit. The influence of the degree distribution of the nodes is naturally taken into account. For simple network topologies we solve the model analytically, the cases of random, small-world and scale-free are studied in detail.