Further results on a class of nonlinear protocols in networked systems

In this paper, we investigate the behaviour of networked systems under two different nonlinear protocols: 1) Pitchfork bifurcation nonlinearity in absolute flow 2) Hopf bifurcation nonlinearity in disagreement flow. The former one is an extension of the results proposed in [13] for the case when individual agents are free to choose a parameter that defines their own dynamics. Based on the eigenvalues of the linearized system, we characterize the set of equilibria that can be achieved under the above protocols. Furthermore, we provide sufficient conditions to achieve consensus for both protocols. Finally, we show that varying the values of the parameter leads to bifurcation for the entire network. For each protocol, we analyze system with two and three agents, and present a characterization of the steady-state behaviour of the entire system.