More on linear differential systems with small delays

Speaker(s)

Urszula Foryś

Affiliation

Uniwersytet Warszawski

Date

May 4, 2011, 4:15 p.m.

Room

room 5820

Seminar

Seminar of Biomathematics and Game Theory Group

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We'll study the aysymptotic dynamics of linear systems of DDEs with small delays. It can be shown that asymptotically such systems behave as the so-called special solutions and for linear DDEs these solutions coincide with fundamental solutions. Moreover, we are able to calculate the limitof X^{-1}(t)x(f)(t) as t tends to infinity, where X(t) is the fundamental matrix (a special solution matrix) and x(f) is the solution to DDe with the initial function f at t=0. This limit can be expressed in terms of the basis of the generalised eigenspace for the formal adjoint equation.

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