Period-doubling/symmetry-breaking mode interactions in iterated maps |
| |
Authors: | PJ Aston H Mir |
| |
Institution: | aDepartment of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, UK |
| |
Abstract: | We consider iterated maps with a reflectional symmetry. Possible bifurcations in such systems include period-doubling bifurcations (within the symmetric subspace) and symmetry-breaking bifurcations. By using a second parameter, these bifurcations can be made to coincide at a mode interaction. By reformulating the period-doubling bifurcation as a symmetry-breaking bifurcation, two bifurcation equations with Z2×Z2 symmetry are derived. A local analysis of solutions is then considered, including the derivation of conditions for a tertiary Hopf bifurcation. Applications to symmetrically coupled maps and to two coupled, vertically forced pendulums are described. |
| |
Keywords: | Mode interaction Period-doubling bifurcation Symmetry-breaking bifurcation Coupled maps |
本文献已被 ScienceDirect 等数据库收录! |
|