AI Article Synopsis
- The paper explores how symmetries and stability interact within nonlinear dynamical systems and networks, aiming to improve analysis and control.
- It integrates traditional symmetry results with new convergence methods from nonlinear contraction theory and virtual dynamical systems.
- Examples include genetic networks where symmetries lead to specific patterns of synchrony and network motifs, demonstrating the practical implications of these theoretical findings.
Article 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.
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| http://dx.doi.org/10.1103/PhysRevE.84.041929 | DOI Listing |
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