Geodesic
On the location of some characteristic quasipolinomial roots
Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 1, pp. 74-84

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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.
Mots-clés : quasi-polynomial
Keywords: D-partition method, asymptotic representation. 
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     title = {On the location of some characteristic quasipolinomial roots},
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D. S. Glyzin; E. P. Kubyshkin; A. R. Moryakova. On the location of some characteristic quasipolinomial roots. Modelirovanie i analiz informacionnyh sistem, Tome 22 (2015) no. 1, pp. 74-84. http://geodesic.mathdoc.fr/item/MAIS_2015_22_1_a4/