Скачать или смотреть Ian Stewart - Hidden symmetries in lattice networks

Name: Ian Stewart
Title: Hidden symmetries in lattice networks
Date: 2023-10-05 @2:00 PM

Abstract: Networks of coupled dynamical systems are a current topic of research in many areas of science. The network topology influences the generic dynamic phenomena, often in curious ways. A fundamental example is synchrony, when two or more nodes have the same time series. Patterns of synchrony in networks of coupled dynamical systems can be represented as colorings, in which nodes with the same color are synchronous. Balanced colorings, where nodes of the same color have color-isomorphic input sets, determine robust synchrony patterns, and define a ‘quotient network’ whose dynamics gives that of the synchronous clusters. Subgroups of the symmetry group of the network lead to balanced colorings, but the converse is false.
We consider doubly periodic balanced colorings of the square and hexagonal lattices with nearest-neighbor coupling, and classify the `exotic’ cases where the quotient network has extra automorphisms not induced from automorphisms of the lattice. These comprise some simple infinite families and a few isolated exceptions. The results have unexpected implications for bifurcations to doubly periodic patterns in lattice models

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