Symmetries, stability, and control in nonlinear systems and networks
Symmetries, stability, and control in nonlinear systems and networks
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DOI：
10.1103/physreve.84.041929
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发表时间：
2011-10-24
影响因子：
2.4
通讯作者：
Slotine, Jean-Jacques E.
中科院分区：
文献类型：
--
作者：
Russo, Giovanni;Slotine, Jean-Jacques E.
本文讨论了非线性动力系统和网络的分析和控制中对称性和稳定性的相互作用。具体来说，它结合了标准的对称性和等方差与最近的收敛分析工具的基础上非线性收缩理论和虚拟动力系统。这种结构属性（对称性）和收敛属性（收缩）之间的协同作用是在网络图案的背景下产生的，例如，在遗传网络中，从不变性到环境对称性，以及在网络中施加不同的同步模式。
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.