Nonlinear coupling near a degenerate Hopf (Bautin) bifurcation

被引:19
作者
Drover, JD [1 ]
Ermentrout, B [1 ]
机构
[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
关键词
Bautin bifurcation; subcritical Hopf bifurcation; bistability; traveling waves; localized pulses;
D O I
10.1137/S0036139902412617
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A nonlinearly coupled system of bistable (fixed point and limit cycle) differential equations is analyzed. The nonlinear equations arise from the first several terms in the normal form expansion near a Bautin bifurcation. Existence and stability of in-phase and out-of-phase periodic solutions to a pair of identical systems are explored. Existence, uniqueness, and stability of traveling wave solutions from a stable rest state to a stable periodic solution are proved for the associated evolution/convolution equation. Numerical simulations suggest some interesting patterns in regimes where waves no longer exist. The results are shown to hold for a nonreduced conductance-based model.
引用
收藏
页码:1627 / 1647
页数:21
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