[Impulse circulation in an excitable medium. Critical size of the closed circuit].
Periodical regimes of impulse circulation are studied for the system of two differential equations Exixi-vE-F(E)-g=0, vg=epsilon(phi(E)-g),(epsilon less than 1), which describes stationary propagation of the impulse with the velocity upsilon. Analytical expressions are obtained for the minimal size of the closed circuit (lambdamin) and minimal circulation velocity (upsilonmin). It has been found that when the circuit size was close to lambdamin, the impulse became relaxed; it means that the plateau lenght was close to the front length. It was shown that lambdamin was practically independent of the small parameter epsilon. In case of the approximation of f(E) by the piecewise N-shaped function with an incident region --Kf(E--alpha), and phi(E) by the linear function KgE, the increase of lambdamin takes place with an increase of alpha and Kg parameters, and a decrease of Kf (fig. 4). Such a change in the parameters brings about a decrease (instead of an intuitively expected increase!) of the stationary velocity of normal impulse propagation.
D001145:Arrhythmias, Cardiac / Q000503:physiopathology; D004594:Electrophysiology; D006321:Heart / Q000502:physiology* / Q000503:physiopathology; D008433:Mathematics; D008954:Models, Biological; D010507:Periodicity
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