Kinematics of wave segments moving through a weakly excitable medium

. Traveling wave segments represent typical spatio-temporal patterns in various active media. In particular they appear by a clustering of interacting active Brownian particles under a global constrain. Wave segments are intrinsically unstable and define a separatrix between spiral wave behavior and contracting wave segments. A kinematical model is developed to describe evolution of a wave segment shape during its stabilization by a global feedback to the medium excitability. It is also applied to specify the relationships between the medium excitability and the asymptotic shape of the stabilized wave segment. The model predictions are compared with results from numerical simulations of the underlying reaction-diffusion system.