Asymptotic properties of solutions of real two-dimensional differential systems with a finite number of constant delays. (English) Zbl 1157.34356

Rebenda, Josef

Mem. Differ. Equ. Math. Phys. 41, 97-114 (2007).

Summary: Stability and asymptotic properties of a real two-dimensional system \[ x'(t)={\mathbf{A}}(t) x(t) + \sum \limits_{j=1}^{n} {\mathbf{B}}_{j} (t) x (t-r_{j}) + {\mathbf{h}} (t,x(t),x(t-r_{1}), \dots, x(t-r_{n})) \] are studied, where \(r_{1}> 0, \dots, r_{n}>0\) are constant delays, \({\mathbf{A, B}}_{1}, \dots, {\mathbf{B}}_{n}\) are matrix functions and h is a vector function. A generalization of results on stability of a two-dimensional differential system with one constant delay is obtained by using the methods of complexification and Lyapunov–Krasovskiǐ functional.

MSC:

34K20

Stability theory of functional-differential equations

Keywords:

stability; asymptotic behaviour; two-dimensional system with delay