| Name |
Zalman Balanov |
| Country |
USA |
| Email |
balanov@utdallas.edu |
| Co-Author(s) |
E. Hooton, W. Krawcewicz, D. Rachinskii, A. Zhezherun |
| Submit Time |
2014-03-03 16:31:20 |
Session |
Special Session 103: Periodic solutions for dynamical systems
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| Contents |
| The standard approach to study symmetric Hopf bifurcation phenomenon is based on the
usage of the equivariant singularity theory developed by M. Golubitsky et al.
In this talk, we present the equivariant degree theory based method which is
complementary to the equivariant singularity approach. Our method allows systematic
study of symmetric Hopf bifurcation problems in non-smooth/non-generic equivariant settings.
The exposition is focused on a network of eight identical van der Pol
oscillators with hysteresis memory, which are coupled in a cube-like configuration leading to
$S_4$-equivariance. The hysteresis memory is the source of non-smoothness and of the presence of an infinite dimensional phase space without local linear structure. Symmetric properties and multiplicity of bifurcating branches of periodic solutions are discussed in the context showing a direct link between the physical properties and the equivariant topology underlying this problem. The global behavior of bifurcating branches is also discussed. |
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