Nonlinear Coupling near a Degenerate Hopf (Bautin) Bifurcation

  • Ermentrout B
  • Drover J
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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.

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  • Bard Ermentrout

  • Jonathan D. Drover

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