On nonlinear singularly perturbed problems in biology

The paper studies a quasi-linear problem with singular perturbation, presented by means of a system of ordinary differential equations. The problem can be applied to model the heartbeat and nerve impulse propagation. The authors develop a constructive algorithm that can be used for evaluating the eigenvalues of the system matrix and indicate conditions of its applicability. They also find relations among given parameters under which the matrix can be reduced to a diagonal matrix. Conditions under which the trivial solution of the problem is asymptotically stable are presented. Two applied examples that illustrate the results obtained conclude the paper.

Авторы
Konyaev Yu.A. , Bezyaev V.I. , Filippova O.N.
Редакторы
Hritonenko Natali
Издательство
Федеральное государственное бюджетное учреждение "Российская академия наук"
Номер выпуска
9
Язык
Английский, Русский
Страницы
107-115
Статус
Опубликовано
Номер
22
Том
22
Год
2010
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Avakov E.R., Arutyunov A.V., Izmailov A.F., Venets Vladimir I.
Журнал вычислительной математики и математической физики. Федеральное государственное бюджетное учреждение "Российская академия наук". 2004.