maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2015-3-420-438mais-260Research ArticleОригинальные статьиArticlesУСТОЙЧИВОСТЬ НЕПРЕРЫВНЫХ ВОЛН ДЛЯ МОДЕЛИ ПОЛУПРОВОДНИКОВОГО ЛАЗЕРА С БОЛЬШИМ ЗАПАЗДЫВАНИЕМSTABILITY OF CW SOLUTIONS OF SEMICONDUCTOR LASER WITH LARGE DELAYКащенкоА. А.KashchenkoA. A.

Кащенко Александра Андреевна, аспирант, orcid.org/0000-0003-3823-9351

sa-ahr@yandex.ruЯрославский государственный университет им. П. Г. ДемидоваРоссияP.G. Demidov Yaroslavl State UniversityRussian Federation201520062015223420438Copyright © Кащенко А.А., 20152015Кащенко А.А.Kashchenko A.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/260

В данной работе решается задача существования и устойчивости непрерывных волн для модели полупроводникового лазера. Эта модель была предложена Лэнгом и Кобаяши и имеет вид двух дифференциальных уравнений с запаздыванием. Время запаздывания предполагается достаточно большим. Исследуется вопрос существования непрерывных волн для модели Лэнга–Кобаяши. Построено специальное множество I, зависящее от всех параметров задачи. Условие существования непрерывных волн состоит в том, что ” главная часть“ решений должна лежать на множестве I. Найдены достаточные условия устойчивости и неустойчивости непрерывных волн при достаточно больших значениях параметра запаздывания. В случае нулевого коэффициента уширения линии найдены необходимые и достаточные условия устойчивости. Изучено расположение областей устойчивости на множестве I. Доказано, что в случае нулевого коэффициента уширения линии на множестве I может быть не более одной области устойчивости, найдены необходимые и достаточные условия ее существования.

In this paper the problem of existence and stability of continuous waves in a semiconductor laser model is studied. This model was proposed by Lang and Kobayashi and has the form of two differential equations with delay. The delay time is assumed to be large. We study the existence of continuous waves in the Lang-Kobayashi model. A special set I depending on all parameters of the problem is built. The condition of existence of continuous waves is that the ”‘main parts”’ of solutions must be located on the set I. Sufficient conditions of stability and instability of continuous waves are found for all sufficiently large values of delay. In the case of a zero linewidth enhancement factor the necessary and sufficient conditions of stability are found. Location of stability regions on the sets I is studied. It is proved that in the case of the zero linewidth enhancement factor the number of regions of stability on the set I is less than two. Necessary and sufficient conditions of existence of stability regions on the set I are found in this case.

уравнение Лэнга–Кобаяшибольшое запаздываниелазерная динамикаустойчивостьLang Kobayashi equationlarge delaylaser dynamicsstabilityЯрГУYaroslavl State UniversityReferencesКащенко А. А., “Устойчивость простейших периодических решений в уравнении Стюарта-Ландау с большим запаздыванием”, Моделирование и анализ информационных систем, 19:3 (2012), 136–141; English transl.: Kashchenko A. A., “Stability of the Simplest Periodic Solutions in the Stuart-Landau Equation with Large Delay”, Automatic Control and Computer Sciences, 47:7 (2013), 566–570.Кащенко А. А., “Устойчивость простейших периодических решений в уравнении Стюарта-Ландау с большим запаздыванием”, Моделирование и анализ информационных систем, 19:3 (2012), 136–141; English transl.: Kashchenko A. A., “Stability of the Simplest Periodic Solutions in the Stuart-Landau Equation with Large Delay”, Automatic Control and Computer Sciences, 47:7 (2013), 566–570.Кащенко А. 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The authors declare that there are no conflicts of interest present.