On Bifurcations in Nonlinear Consensus Networks
The theory of consensus dynamics is widely employed to study various linear behaviors in networked control systems. Moreover, nonlinear phenomena have been observed in animal groups, power networks and in other networked systems. These observations inspire the development in this paper of three novel approaches to define distributed nonlinear dynamical interactions. The resulting dynamical systems are akin to higher-order nonlinear consensus systems. Over connected undirected graphs, the resulting dynamical systems exhibit various interesting behaviors that we rigorously characterize.
KeywordsConsensus network Networked systems Bifurcation theory
Mathematics Subject Classification (2000)34C23 34K18 68M12
- Papachristodoulou, A., Jadbabaie, A.: Synchronization in oscillator networks with heterogeneous delays, switching topologies and nonlinear dynamics. In: IEEE Conf. on Decision and Control, San Diego, CA, December 2006, pp. 4307–4312 (2006) Google Scholar
- Poulakakis, I., Scardovi, L., Leonard, N.E.: Coupled stochastic differential equations and collective decision making in the Two-Alternative Forced-Choice task. In: American Control Conference, pp. 69–74 (2010) Google Scholar
- Srivastava, V., Moehlis, J., Bullo, F.: On bifurcations in nonlinear consensus networks. In: American Control Conference, Baltimore, MD, June 2010, pp. 1647–1652 (2010) Google Scholar
- Strogatz, S.H.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Perseus Books Group, New York City (2000) Google Scholar