1997/09/01 by G Dangelmayr, Gerhard Dangelmayr, J Hettel +3 · 1 citation
Computer Science · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #stochastic dynamics and bifurcation
paper · doi:10.1088/0951-7715/10/5/006
openalex publication_date 1997/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The steady-state reflection-breaking bifurcation from a circle of nontrivial equilibria in O(2)-equivariant systems results in a pair of travelling waves. When the continuous part of the group O(2) is weakly broken, the corresponding instability may lead to nonsymmetric but steady states. The transition from this state to the travelling wave state with increasing bifurcation parameter is complex, and typically involves sequences of global bifurcations. The possible scenarios are described in detail and the results are related to the dynamics associated with parity-breaking instabilities of spatially periodic patterns in inhomogeneous systems.