Open AccessSimplification of weakly nonlinear systems and analysis of cardiac activity using them
Author(s) -
Ірада Джалладова,
Miroslava Růžičková
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021191
Subject(s) - normalization (sociology) , nonlinear system , mathematics , transformation (genetics) , differential equation , algorithm , computer science , mathematical analysis , biochemistry , chemistry , physics , quantum mechanics , sociology , anthropology , gene
The paper deals with the transformation of a weakly nonlinear system of differential equations in a special form into a simplified form and its relation to the normal form and averaging. An original method of simplification is proposed, that is, a way to determine the coefficients of a given nonlinear system in order to simplify it. We call this established method the degree equalization method, it does not require integration and is simpler and more efficient than the classical Krylov-Bogolyubov method of normalization. The method is illustrated with several examples and provides an application to the analysis of cardiac activity modelled using van der Pol equation.