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Pacemakers in a reaction-diffusion mechanics system. (English) Zbl 1115.92004
Summary: Nonlinear waves of excitation are found in various biological, physical and chemical systems and are often accompanied by deformations of the medium. We numerically study wave propagation in a deforming excitable medium using a two-variable reaction-diffusion system coupled with equations of continuum mechanics. We study the appearance and dynamics of different excitation patterns organized by pacemakers that occur in the medium as a result of deformation. We also study the interaction of several pacemakers with each other and the characteristics of pacemakers in the presence of heterogeneities in the medium. We found that mechanical deformation not only induces pacemakers, but also has a pronounced effect on spatial organization of various excitation patterns. We show how these effects are modulated by the size of the medium, the location of the initial stimulus, and the properties of the reaction-diffusion-mechanics feedback.

MSC:
92C05 Biophysics
35K57 Reaction-diffusion equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
92C10 Biomechanics
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