کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4609274 1338503 2016 36 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Graph fibrations and symmetries of network dynamics
ترجمه فارسی عنوان
فیبرهای گراف و تقارن پویایی شبکه
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

Dynamical systems with a network structure can display remarkable phenomena such as synchronisation and anomalous synchrony breaking. A methodology for classifying patterns of synchrony in networks was developed by Golubitsky and Stewart. They showed that the robustly synchronous dynamics of a network is determined by its quotient networks. This result was recently reformulated by DeVille and Lerman, who pointed out that the reduction from a network to a quotient is an example of a graph fibration. The current paper exploits this observation and demonstrates the importance of self-fibrations of network graphs. Self-fibrations give rise to symmetries in the dynamics of a network. We show that every network admits a lift with a semigroup or semigroupoid of self-fibrations. The resulting symmetries impact the global dynamics of the network and can therefore be used to explain and predict generic scenarios for synchrony breaking. Also, when the network has a trivial symmetry groupoid, then every robust synchrony in the lift is determined by symmetry. We finish this paper with a discussion of networks with interior symmetries and nonhomogeneous networks.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 261, Issue 9, 5 November 2016, Pages 4861–4896
نویسندگان
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