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Mathematical model

We use the FitzHugh-Nagumo excitable media model in the form, Winfree [25],

  equation38

where D is a diffusion coefficient, tex2html_wrap_inline852 is the Laplacian, F(t) is an external forcing, and the non-linear terms are

  equation48

In polar coordinates r and tex2html_wrap_inline858 the Laplacian reads

  equation53

The first equation in (1) describes the fast process of formation and propagation of the wave front; the second equation describes the local recovery of the properties of the medium. In the context of biological excitable tissues the variables u and v are commonly interpreted as the membrane potential of the cell, and the slow repolarizing currents through the membrane; the F(t) can be interpreted as, for instance, an external electric current.



Vadim Biktashev
Fri Apr 4 17:38:59 GMT 1997