Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry

Mode Interactions With Symmetry

“…To draw the bifurcation diagrams, we restrict the equations to Fix(S3) = R. We, choose a>0 and b, <0 so that we have case (2), that is, there exist no solutions for A<0 and there are two solutions for A>0, one stable and one Note that theZ2-symmetric branch is in the plane defined by a-x…”

“…y-mode x-mode mixed-mode mixed-mode y-mode x-mode 00 y-mode x-n eTde i ihixe -mode (2) x-mode e y-mode 00a y-mode -x-mode (3)…”

“…We then have two representations of 0(3) on V1, according 2 to whether the element of order 2 in Zc acts as plus or minus the identity. We study the interactions involving the modes of order I-0,1 =I and…”

Nonlinear Marangoni convection in circular and elliptical cylinders

“…25,26 The most dramatic feature of this interaction is the presence, in certain parameter regimes, of structurally stable heteroclinic cycles connecting the m = 2 state with its rotations by / 4. Such cycles have been observed in A = 2.5 containers by Johnson and Narayanan 5 and reproduced within weakly nonlinear theory by Dauby et al;24 see also Ref.…”

Control and stabilization of systems with homoclinic orbits

“…In this paper we consider a model of 2 complex dimensions or 4 real dimensions which was analyzed in Armbruster, Guckenheimer and Holmes [1988]. While this model is of too low an order for really good physical representation, it does contain many of the features of the higher order models, in particular exhibiting asymptotically stable and structurally stable heteroclinic cycles in certain regions of the phase space.…”