Propagation Failure in Excitable Media

Abstract

We study a mechanism of pulse propagation failure in excitable media where stable traveling pulse solutions appear via a subcritical pitchfork bifurcation. The bifurcation plays a key role in that mechanism. Small perturbations, externally applied or from internal instabilities, may cause pulse propagation failure (wave breakup) provided the system is close enough to the bifurcation point. We derive relations showing how the pitchfork bifurcation is unfolded by weak curvature or advective field perturbations and use them to demonstrate wave breakup. We suggest that the recent observations of wave breakup in the Belousov-Zhabotinsky reaction induced either by an electric field or a transverse instability are manifestations of this mechanism.

8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.html

References in corpus (7)

• Pattern Formation in Dissipative Nonvariational Systems: The Effects of Front Bifurcations
• From Labyrinthine Patterns to Spiral Turbulence
• Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
• Interface Proliferation and the Growth of Labyrinths in a Reaction-Diffusion System
• General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems
• Dynamic Front Transitions and Spiral-Vortex Nucleation
• The Dynamics of Curved Fronts: Beyond Geometry

Cited by in corpus (4)

• A new spatio-temporal description of long-delayed systems: ruling the dynamics
• Drifting solitary waves in a reaction-diffusion medium with differential advection
• Catalytic membrane reactor model as a laboratory for pattern emergence in reaction-diffusion-advection media
• Subcritical Pitchfork Bifurcation Transition of a Single Nanoparticle in Strong Confinement