Abstract:
The article presents a study of the autowave processes model based on a parabolic system of partial differential equations, the Aliev–Panfilov model. The model is widely used for studying the characteristics of myocardial excitation waves during the cardiac arrhyth mias. Our previous studies, carried out for a two-dimensional version of this model with changing one of its parameters in a wide range of values, was resulted in detecting the specific transient processes for the systems near the bifurcation points. The specific transient processes were interpreted as the stability loss delay (bifurcation memory), which has been studied quite well for systems of ordinary differential equations. This paper presents a study of the specified model when changing two of its parameters. Using quantitative analysis of the behavior of a two-dimensional autowave vortex in a homogeneous isotropic model medium, we construct a parametric portrait of the two-dimensional version of the Aliev–Panfilov model, with indicating on it the position of the bifurcation boundary and the bifurcation spot (that is, the region of parameters in which bifurcation memory phenomena are observed). The difference between this model and classical models of autowave processes is demonstrated. Some special cases of autowave vortex behavior are presented, which have not been previously described in the literature. The relationship between the features of the electrocardiogram and the behavior of the autowave vortex in the model myocardium was demonstrated before, taking into account the bifurcation memory. Although the presented results have been obtained theoretically, they may be useful in the clinical practice of cardiologists. The publication is intended primarily for specialists in the fields of mathematical biology, mathematical modeling and biophysics.
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