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APS » Journals » Phys. Rev. A » Volume 46 » Issue 8
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Phys. Rev. A 46, 5054–5062 (1992)

Symmetry-breaking bifurcations in one-dimensional excitable media

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Mark Kness
Center for Nonlinear Dynamics and Department of Physics, University of Texas, Austin, Texas 78712

Laurette S. Tuckerman
Center for Nonlinear Dynamics and Department of Mathematics, University of Texas, Austin, Texas 78712

Dwight Barkley
Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544

Received 6 April 1992; published in the issue dated October 1992

A two-species reaction-diffusion model is used to study bifurcations in one-dimensional excitable media. Numerical continuation is used to compute branches of traveling waves and periodic steady states, and linear stability analysis is used to determine bifurcations of these solutions. It is shown that the sequence of symmetry-breaking bifurcations which lead from the homogeneous excitable state to stable traveling waves can be understood in terms of an O(2)-symmetric normal form.

© 1992 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.46.5054
DOI:
10.1103/PhysRevA.46.5054
PACS:
82.20.Wt, 82.20.Mj, 02.20.+b
 
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