Analysis of a Non-linear Partial Difference Equation, and Its Application to Cardiac Dynamics

Autor:	Michael D. Stubna, Robert F. Gilmour, Richard H. Rand
Rok vydání:	2002
Předmět:	Singular perturbation Algebra and Number Theory Computer simulation Applied Mathematics Mathematical analysis Poincaré–Lindstedt method Periodic function symbols.namesake Nonlinear system Singularity symbols Analysis Bifurcation Multiple-scale analysis Mathematics
Zdroj:	Journal of Difference Equations and Applications. 8:1147-1169
ISSN:	1563-5120 1023-6198
Popis:	A model of a strip of cardiac tissue consisting of a one-dimensional chain of cardiac units is derived in the form of a non-linear partial difference equation. Perturbation analysis is performed on this equation, and it is shown that regular perturbations are inadequate due to the appearance of secular terms. A singular perturbation procedure known as the method of multiple scales is shown to provide good agreement with numerical simulation except in the neighborhood of a singularity of the slow flow. The perturbation analysis is supplemented by a local numerical simulation near this singularity. The resulting analysis is shown to predict a "spatial bifurcation" phenomenon in which parts of the chain may be oscillating in period-2 motion while other parts may be oscillating in higher periodic motion or even chaotic motion.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::32c44abb3263b75bd1ad27ee967eca4d https://doi.org/10.1080/1023619021000054006 Zobrazit plný text záznamu