SN-equivariant symmetry-breaking bifurcations

被引：12
|
作者：
Elmhirst, T [1 ]
机构：
[1] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2004年 / 14卷 / 03期
关键词：
symmetry-breaking; bifurcation theory; equivariant dynamics; symmetry group; Liapunov-Schmidt reduction;
D O I：
10.1142/S0218127404009697
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
I analyze generic symmetry-breaking bifurcations of S-N-equivariant vector fields (where genericity is in the restricted space of S-N-equivariant systems). The normal form for the Liapunov-Schmidt reduced bifurcation problem is derived, and its codimension 1 symmetry-breaking bifurcations are investigated. Branch equations are given along with the conditions for stability, and the parameter space is partitioned accordingly. Applications in complex systems theory are suggested in which the dynamics of S-N-equivariant systems are used to model the emergent behavior of systems of multiple interacting agents.
引用
收藏
页码：1017 / 1036
页数：20
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