A numerical study of resonant regimes near the points of codimension-2 bifurcation in Couette-Taylor problem

Abstract

The investigation of codimension-2 bifurcations in the systems with cylindric symmetry enables us to find out new types of secondary regimes branching off from the symmetric regimes. The central manifold approach combined with the reduction to the normal form lead to the so called amplitude systems.These ODE systems describe the nonlinear interaction between the neutral modes and include always several nonlinear terms due to so called intrinsic resonances. However, sometimes additional resonances appear. We present the results of investigation of interaction between two nonaxisymmetric neutral modes in the Couette--Taylor problem in the intrinsic resonances case (Res 0) and one of six additional resonances (Res 3).