Symmetries, stability, and control in nonlinear systems and networks

Giovanni Russo and Jean-Jacques E. Slotine

Phys. Rev. E 84, 041929 – Published 24 October 2011; Erratum Phys. Rev. E 85, 059902 (2012)

Abstract

This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems. This synergy between structural properties (symmetries) and convergence properties (contraction) is illustrated in the contexts of network motifs arising, for example, in genetic networks, from invariance to environmental symmetries, and from imposing different patterns of synchrony in a network.

Received 31 October 2010

DOI:https://doi.org/10.1103/PhysRevE.84.041929

Erratum

Erratum: Symmetries, stability, and control in nonlinear systems and networks [Phys. Rev. E 84, 041929 (2011)]

Giovanni Russo and Jean-Jacques E. Slotine

Phys. Rev. E 85, 059902 (2012)

Authors & Affiliations

Giovanni Russo^1,* and Jean-Jacques E. Slotine^2,†

¹Department of Systems and Computer Engineering, University of Naples Federico II, Italy
²Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

^*Also at Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. giovanni.russo2@unina.it
^†jjs@mit.edu

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Vol. 84, Iss. 4 — October 2011

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Physical Review E

covering statistical, nonlinear, biological, and soft matter physics