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@inproceedings{720899, author = {Kalas, Josef}, address = {Bratislava}, booktitle = {Proceedings of Equadif-11}, keywords = {Delayed differential equations; asymptotic behaviour; stability; boundedness of solutions; two-dimensional systems; Lyapunov method; Wazewski topological principle.}, language = {eng}, location = {Bratislava}, isbn = {978-80-227-2624-5}, pages = {171-180}, publisher = {Comenius University, Bratislava, Slovakia}, title = {Asymptotic properties of a two-dimensional differential system with delay}, year = {2007} }
TY - JOUR ID - 720899 AU - Kalas, Josef PY - 2007 TI - Asymptotic properties of a two-dimensional differential system with delay PB - Comenius University, Bratislava, Slovakia CY - Bratislava SN - 9788022726245 KW - Delayed differential equations KW - asymptotic behaviour KW - stability KW - boundedness of solutions KW - two-dimensional systems KW - Lyapunov method KW - Wazewski topological principle. N2 - The asymptotic nature of the solutions of a real two-dimensional system of retarded differential equations x'(t) = A(t)x(t) + B(t)x(t-r)+ h(t,x(t),x(t-r)), where r>0 is a constant delay, A, B and h being matrix functions and a vector function, respectively, is examined. The method of complexification transforms this system to one equation with complex-valued coefficients. Stability and the asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle. ER -
KALAS, Josef. Asymptotic properties of a two-dimensional differential system with delay. In \textit{Proceedings of Equadif-11}. Bratislava: Comenius University, Bratislava, Slovakia, 2007, s.~171-180. ISBN~978-80-227-2624-5.
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