On the Floquet multipliers of periodic solutions to non-linear functional differential equations

For periodic solutions to the autonomous delay differential equation x′(t) =-μx(t) + f(x(t-1)) with rational periods we derive a characteristic equation for the Floquet multipliers. This generalizes a result from an earlier paper where only periods larger than 2 were considered. As an application we obtain a criterion for hyperbolicity of certain periodic solutions, which are rapidly oscillating in the sense that the delay 1 is larger than the distance between consecutive zeros. The criterion is used to find periodic orbits which are unstable and hyperbolic. An example of a non-autonomous periodic linear delay differential equation with a monodromy operator which is not hyperbolic shows how subtle the conditions of the hyperbolicity criteria in the present paper and in its predecessor are. We also derive first results on Floquet multipliers in case of irrational periods. These are based on approximations by periodic solutions with rational periods. © 2006 Springer Science+Business Media, Inc.

Авторы
Skubachevskii A.L. 1 , Walther H.-O.2
Номер выпуска
2
Язык
Английский
Страницы
257-355
Статус
Опубликовано
Том
18
Год
2006
Организации
  • 1 Peoples' Friendship University of Russia, Ordzhonikidze str., 3, Moscow 117923, Russian Federation
  • 2 Mathematisches Institut, Universität Gießen, Arndtstr. 2, D 35392 Gießen, Germany
Ключевые слова
Delay differential equation; Floquet multipliers; Hyperbolic periodic orbit; Periodic solution
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/3381/