On the Movement of Excitation Wave Breaks

Yu.E. Elkin , V.N. Biktashev & A.V. Holden

Institute for Mathematical Problems in Biology, Pushchino, Moscow Region, 142292, Russia
Department of Physiology, University of Leeds, Leeds LS2 9JT, UK
Author to whom correspondence should be addressed

Abstract:

Movement of excitation waves in active media in some cases can be described by a kinematic approach in terms of movement of curves, the wave crests, by neglecting other details such as wave profile and refractoriness. Of special interest are broken waves, e.g. spiral waves. In this case, additional equations for the wave tip movement are required. We derive such equations by singular perturbation techniques. These equations differ from those proposed earlier from semi-phenomenological arguments [10, 11], are more complicated and diverse and admit a broader variety of solutions. As an illustration, we apply these equations to the problem of a stationary rotating spiral wave. In this particular example, the `traditional' equations have happened to be a special case.

• Introduction
• Derivation of the wave tip motion equations
• The stationary spiral wave
  • Problem formulation and general solution.
  • The generic case.
  • The case of zero tip growth rate.
• Discussion.
• References