1 N ov 1 99 9 The geometry of bifurcation surfaces in parameter space . I . A walk through the pitchfork

ar X iv : d g - ga / 9 51 10 05 v 5 2 0 N ov 1 99 5 MODIFIED NOVIKOV – VESELOV EQUATION AND DIFFERENTIAL GEOMETRY OF SURFACES

The Non-smooth Pitchfork Bifurcation

The bifurcations of strange nonchaotic attractors in quasi-periodically forced systems are poorly understood. A simple two-parameter example is introduced which unifies previous observations of the non-smooth pitchfork bifurcation. There are two types of generalized pitchfork bifurcation which occur in this example, and the corresponding bifurcation curves can be calculated analytically. The ex...

Patterns of oscillation in a Ring of Identical Cells with Delayed Coupling

We investigate the behaviour of a neural network model consisting of three neurons with delayed self and nearest-neighbour connections. We give analytical results on the existence, stability and bifurcation of nontrivial equilibria of the system. We show the existence of codimension two bifurcation points involving both standard and D3-equivariant, Hopf and pitchfork bifurcation points. We use ...

ar X iv : h ep - t h / 99 11 12 0 v 1 1 6 N ov 1 99 9 Coset - Space String Compactification Leading To 14 Subcritical Dimensions

Using sigma-model approach, we study a class of coset spaces with torsion which compactify the D = 26 closed bose-string theory. Requiring also that massless chiral fermions arise from the geometry/topology of coset space, we are left with the unique possibility: it implies D = 14 subcritical dimensions and certain isometry group.

On the bifurcation structure of axisyrnmetric vortex breakdown in a constricted pipe

The bifurcation structure is presented for an axisymmetric swirling flow in a constricted pipe, using the pipe geometry of Beran and Culick [J. Fluid Mech. 242, 491 (1992)]. The flow considered has been restricted to a two-dimensional parameter space comprising the Reynolds number Re and the relative swirl V, of the incoming swirling flow. The bifurcation diagram is constructed by solving the t...