Abstract
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.
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Communicated by R. Sepulchre.
A preliminary version of this work (Srivastava et al. 2010) was presented at the 2010 American Control Conference, Baltimore, MD, USA.
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Srivastava, V., Moehlis, J. & Bullo, F. On Bifurcations in Nonlinear Consensus Networks. J Nonlinear Sci 21, 875–895 (2011). https://doi.org/10.1007/s00332-011-9103-4
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DOI: https://doi.org/10.1007/s00332-011-9103-4