In this work, we propose an emergent dynamics based tool to approximate the synchronized behavior in large networks of interconnected linear systems with switching interconnection topologies and linear coupling. We assume that the networks are heterogeneous, but the states of all systems are of the same dimension. The goal of this paper is to show that, in the case of sufficiently large coupling gains, the network is practically synchronized, and its' synchronized behavior can be approximated by a reduced order switching system independent of the control gains. The results are ensured for strongly connected networks under fairly mild assumptions by introducing a minimum dwell-time between two consecutive switches. Numerical simulations illustrate the theoretical results.

We address formally the problem of opinion dynamics when the social network composed of conformists and contrarians are not only influenced by their neighbors, but also by an external influential entity referred to as a marketer. The population of contrarians tries to have an opinion that is the opposite of the opinion held by the conformists. The influential entity tries to sway the overall opinion as close as possible to the desired opinion by using a specific influence budget. The main technical issue addressed is finding how the marketer should allocate its budget among the agents such that the agents' opinion will be as close as possible to the desired opinion while taking into account the behavior of the contrarian population. Our main results show that the marketer has to prioritize certain agents over others based on their initial condition, their influence power in the social graph and the population class they belong to. Numerical examples illustrate the analysis.

No abstract