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Free keywords:
pattern formation, nonlinear dynamics, wave segments, excitable medium
Abstract:
The propagation velocity and the shape of a stationary propagating wave segment are determined analytically for excitable media supporting excitation waves with trigger fronts and phase backs. The general relationships between the mediumʼs excitability and the wave segment parameters are obtained in the framework of the free boundary approach under quite usual assumptions. Two universal limits restricting the region of existence of stabilized wave segments are found. The comparison of the analytical results with numerical simulations of the well-known Kessler–Levine model demonstrates their good quantitative agreement. The findings should be applicable to a wide class of systems, such as the propagation of electrical waves in the cardiac muscle or wave propagation in autocatalytic chemical reactions, due to the generality of the free-boundary approach used.
