SN-equivalent symmetry-breaking bifurcations
Elmhirst, Toby (2004) SN-equivalent symmetry-breaking bifurcations. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 14 (3). pp. 1017-1036.
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I analyze generic symmetry-breaking bifurcations of SN-equivariant vector fields (where genericity is in the restricted space of SN-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 SN-equivariant systems are used to model the emergent behavior of systems of multiple interacting agents.
|Item Type:||Article (Refereed Research - C1)|
|Keywords:||symmetry-breaking; bifurcation theory; SN-equivariant systems; Taylor expansion; eigenspaces; eigenvalues; equivariant dynamics; symmetry group; Liapunov-Schmidt reduction|
|Date Deposited:||07 Jun 2010 01:37|
|FoR Codes:||01 MATHEMATICAL SCIENCES > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications @ 100%|
|SEO Codes:||97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 100%|