The variables U and V represent the concentrations of the activator and the inhibitor species, respectively.e, a, and b are parameters of the reaction kinetics, and d is the ratio of diffusion coefficients of two species.
Of the two variables, one (u) corresponds to the electric potential across the cell membrane. This variable changes rapidly and has a large diffusion coefficient. The second variable (v) corresponds to ion concentrations, which change slowly and have a small diffusion coefficient (which we set to zero in some cases).
The essential feature of this model is that the evolution of u is a cubic function of u and contains an additive linear term of v. The evolution of v has one term proportional to u and one term proportional to v.
The characteristic feature of excitable media is that if the system is perturbed away from the stable steady state more than a small threshold, the return to the unique stable steady state does not follow a direct path, but proceeds via a long excursion in phase space.
[the next is from Kyoung J. Lee, Phy. Rev. Lett.
79,2907(1997)]
The variables U and V represent the concentrations of
the activator and the inhibitor species, respectively.e,
a, and b are parameters of the reaction
kinetics, and d is the ratio of diffusion coefficients
of two species.
Two different competitions between a spiral and a periodic pacemaker.
Tspiral = 55.4, Tpacemaker
= 66.4 (a), 44.3 (b)
Pararemteres for bulk: e=0.12, a=1.0,
b=20.2,
and d=0.1.
The pacemaker (a small region with a radius of 4 grids) e=0.06,
a=0
(a) b=0.04, d=-0.12(b)
128x128 pixels
The competition between two different wave trains is based solely on
their periods. Two different wave trains upon head-on collision annihilate
each other. Therefore, if one wave train has a smaller period than that
of the second wave train, the spatial location where the collision occurs
would gradually shift toward the source with a longer period and eventually
the slower source would be entrained.The slower one loses its role as a
source for waves.
