A normal form for excitable media

Details A normal form for excitable media A normal form for excitable media

2006-03-14

arxiv.org/abs/nlin/0603032v1

Nonlinear Sciences

Pattern Formation and Solitons

22 pages, accepted for publication in Chaos

Scientific paper

10.1063/1.2168393

We present a normal form for travelling waves in one-dimensional excitable media in form of a differential delay equation. The normal form is built around the well-known saddle-node bifurcation generically present in excitable media. Finite wavelength effects are captured by a delay. The normal form describes the behaviour of single pulses in a periodic domain and also the richer behaviour of wave trains. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with the saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We verify the existence of these bifurcations in numerical simulations. The parameters of the normal form are determined and its predictions are tested against numerical simulations of partial differential equation models of excitable media with good agreement.

Affiliated with

Also associated with

No associations

Rating

A normal form for excitable media does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A normal form for excitable media, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A normal form for excitable media will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-728973