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
相关论文
共 50 条
  • [41] Symmetry-breaking and bifurcation diagrams of fractional-order maps
    Danca, Marius -F.
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 116
  • [42] Efficient manipulation of plasmonic modes in single symmetry-breaking nanocube
    Li, Pengwei
    Wang, Hongfang
    Turup, Zulhumar
    Yang, Xiaoyu
    Wang, Jingyu
    Gao, Min
    APPLIED SURFACE SCIENCE, 2023, 611
  • [43] Symmetry-Breaking Charge Transfer in Boron Dipyridylmethene (DIPYR) Dimers
    Golden, Jessica H.
    Estergreen, Laura
    Porter, Tyler
    Tadle, Abegail C.
    Sylvinson, Daniel M. R.
    Facendola, John W.
    Kubiak, Clifford P.
    Bradforth, Stephen E.
    Thompson, Mark E.
    ACS APPLIED ENERGY MATERIALS, 2018, 1 (03): : 1083 - 1095
  • [44] Numerical analysis on transitions and symmetry-breaking in the wake of a flapping foil
    He, Guo-Yi
    Wang, Qi
    Zhang, Xing
    Zhang, Shu-Guang
    ACTA MECHANICA SINICA, 2012, 28 (06) : 1551 - 1556
  • [45] Endogenous comparative advantage, gains from trade and symmetry-breaking
    Chatterjee, Arpita
    JOURNAL OF INTERNATIONAL ECONOMICS, 2017, 109 : 102 - 115
  • [46] Symmetry breaking bifurcations in the NLS equation with an asymmetric delta potential
    Rusin, Rahmi
    Marangell, Robert
    Susanto, Hadi
    NONLINEAR DYNAMICS, 2020, 100 (04) : 3815 - 3824
  • [47] Symmetry-breaking bifurcation for the Moore-Nehari differential equation
    Kajikiya, Ryuji
    Sim, Inbo
    Tanaka, Satoshi
    NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2018, 25 (06):
  • [48] Hartree-Fock symmetry-breaking in magnesium and nickel porphyrins
    Piqueras, MC
    Rohlfing, CM
    JOURNAL OF MOLECULAR STRUCTURE-THEOCHEM, 1996, 388 : 293 - 297
  • [49] Symmetry-Breaking of Turbulence Structure and Position Identification in Toroidal Plasmas
    Itoh, Kimitaka
    Itoh, Sanae-I
    Nagashima, Yoshihiko
    Yamada, Takuma
    Kosuga, Yusuke
    Fujisawa, Akihide
    PLASMA AND FUSION RESEARCH, 2018, 13
  • [50] UNIQUENESS OF POSITIVE RADIAL SOLUTIONS OF THE BREZIS-NIRENBERG PROBLEM ON THIN ANNULAR DOMAINS ON Sn AND SYMMETRY BREAKING BIFURCATIONS
    Shioji, Naoki
    Watanabe, Kohtaro
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (10) : 4727 - 4770
12345