A Algaba et al 1999 Nonlinearity 12 1177 doi:10.1088/0951-7715/12/4/324
A Algaba
, E Freire
, E Gamero
and A J Rodríguez-Luis![]()
Recommended by A I Neishtadt
A codimension-three unfolding for the
2-symmetric Hopf-pitchfork bifurcation, in the presence of an additional nonlinear degeneracy, is analysed.
Up to ten distinct topological equivalence classes for the unfolding are found. A rich variety of dynamical and bifurcation behaviours is pointed out. Beyond the bifurcations present in the nondegenerate case, we show that the following bifurcations appear locally: Takens - Bogdanov of periodic orbits, degenerate pitchfork of periodic orbits, and global connections involving equilibria and/or periodic orbits.
The local results achieved, extended by means of numerical continuation methods, are used to understand the dynamics of a modified van der Pol - Duffing electronic oscillator, for a certain range of the parameters.
37G15 Bifurcations of limit cycles and periodic orbits
Issue 4 (July 1999)
Received 1 April 1998, in final form 7 April 1999
A Algaba et al 1999 Nonlinearity 12 1177
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