On the Location of Some Characteristic Quasipolinomial Roots

The location of zeros of two characteristic quasi-polynomials arising from studying the differential equations with a retarded argument is considired. The first one originates from the mathematical model of electromagnetic oscillations generator with a delayed feedback, the second one — from the Lan...

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Bibliographic Details
Published inModelirovanie i analiz informacionnyh sistem Vol. 22; no. 1; pp. 74 - 84
Main Authors Glyzin, D. S., Kubyshkin, E. P., Moryakova, A. R.
Format Journal Article
LanguageEnglish
Published Yaroslavl State University 01.02.2015
Subjects
asymptotic representation
d-partition method
quasi-polynomial
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Summary:The location of zeros of two characteristic quasi-polynomials arising from studying the differential equations with a retarded argument is considired. The first one originates from the mathematical model of electromagnetic oscillations generator with a delayed feedback, the second one — from the Lang-Kobayashi system that is a well-known mathematical model of a quantum generator. The D-partition figures are presented in a prameter space and possible critical cases are found out. The large delay case important for applications is considered. In this case, for quasi-polinomial roots obtained are the analytical dependencies on a value reciprocal to the delay, and uniform asymptotical formulas are constructed.
ISSN:1818-1015
2313-5417
DOI:10.18255/1818-1015-2015-1-74-84