On the Location of Some Characteristic Quasipolinomial Roots - D. S. Glyzin; E. P. Kubyshkin; A. R. Moryakova (Моделирование и анализ информационных систем)
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.