对称性破坏
参数空间
分叉
对称(几何)
数学
分岔理论
齐次空间
跨临界分岔
显式对称破缺
干草叉分叉
自发对称破缺
状态空间
统计物理学
数学分析
物理
非线性系统
几何学
量子力学
统计
作者
Antonio Lozano Palacios,Francesco Sorrentino,Amirhossein Nazerian,Visarath In
标识
DOI:10.1142/s0218127423300276
摘要
Emergent behavior in complex networks can be predicted and analyzed via the mechanism of spontaneous symmetry-breaking bifurcation, in which solutions of related bifurcation problems lose symmetry as some parameters are varied, even though the equations that such solutions satisfy retain the full symmetry of the system. A less common mechanism is that of forced symmetry-breaking, in which either a bifurcation problem has symmetry on both the state variables and the parameters, or one where the equations have less symmetry when a certain parameter is varied. In this manuscript, it is shown that in certain networks with parameter mismatches the governing equations remain unchanged when the group of symmetries acts on both the state variables and the parameter space. Based on this observation we study the existence and stability of collective patterns in symmetric networks with parameters mismatches from the point of view of forced symmetry-breaking bifurcations. Treating the parameters as state variables, we perform center manifold reductions, which allow us to understand how the disorder in parameters affects the bifurcation points as well as the stability properties of the ensuing patterns. Theoretical results are validated with numerical simulations.
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