Asymptotic behaviour of real two-dimensional differential system with a finite number of constant delays. (English) Zbl 1169.34051

Rebenda, Josef

Demonstr. Math. 41, No. 4, 845-857 (2008).

The following real two-dimensional system
\[ x'(t) = {\mathbf A}(t) x(t) + \sum_{j=1}^n {\mathbf B}_j(t) x(t-r_j) + {\mathbf h}(t,x(t),x(t-r_1),\dots,x(t-r_n)) \]
is considered, where \(r_j>0\), \(j=1,\dots,n\), \({\mathbf A}\) and \({\mathbf B}_j\) are matrix-valued functions, and \({\mathbf h}\) is a vector function. The stability and asymptotic properties are studied.

Reviewer: Satoshi Tanaka (Okayama)

MSC:

34K25	Asymptotic theory of functional-differential equations
34K20	Stability theory of functional-differential equations
34K12	Growth, boundedness, comparison of solutions to functional-differential equations