Spatial Effects in Active Chemical Systems. I. Model of Leading Center

Abstract

In the Belousov-Zhabotinskii reaction occuring in a homogeneous thin layer (1 -2 mm), the appearance of regions with frequencies greater than that of other spatial points was observed. We suggest this to be a new phenomenon. It was named the leading center, and it must be distinguished from the pacemaker. In this paper a general model of such phenomena is presented. We consider here the distributed (reactiondiffusion) system with three variables. One of them has an S-shaped form of quasistationary characteristics. Diffusion of one component was tä ön into account. The appearance of a region with a stable higher frequency in a system which is autonomous with respect to space coordinates and time, was shown analytically and confirmed by numerical calculations. This model should be treated as a minimal one in the sense that it contains the minimal number of components and diffusion coefficients necessary to obtain the leading center.

Pattern formation arising from wave instability in a simple reaction-diffusion system

“…13,[17][18][19][20] Target patterns have been found to emerge due to large amplitude perturbations of limit cycle bulk oscillations in some reaction-diffusion models. 21,22 They also arise as solutions of the Ginsburg-Landau equations derived in the vicinity of the Hopf-Turing codimension-2 bifurcation. [23][24][25] Still, the wave instability seems to be the most likely cause of TP formation arising from small concentration fluctuations.…”

Basic Mechanisms of Cardiac Arrhythmias

“…In addition, several autowave objects were described under the general title "leading centers" [41,[61][62][63][64][65]. In two-dimensional and three-dimensional excitable media, leading centers emit concentric waves similar to the waves initiated by a pacemaker.…”

“…At least three different mechanisms of leading centers are known from theoretical studies. One of them is described for media consisting of self-oscillatory elements with hard excitation [62]. Such a medium can be at state of rest (i.e.…”

New type of the source of travelling impulses in two-variable model of reaction–diffusion system

“…Therefore, the first models of the leading center were abstract ones. They were based on activator-inhibitor types mechanisms [20,21]. The model constructed by Zhabotinsky and Zaikin [20] consisted of two reaction-diffusion equations of the activator-inhibitor type but the cause of generation of the leading center was difficult to explain.…”

“…The model constructed by Zhabotinsky and Zaikin [20] consisted of two reaction-diffusion equations of the activator-inhibitor type but the cause of generation of the leading center was difficult to explain. In the next abstract model describing the appearance of a target pattern in excitable system of the activator-inhibitor type, one variable was added in order to shift a position of nullcline of the inhibitor from excitable to the oscillatory regime [21].…”