Asymptotic behaviour of a two‐dimensional differential system with non‐constant delay |
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Authors: | Josef Kalas |
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Affiliation: | Department of Mathematics and Statistics, Masaryk University, Kotlá?ská 2, 611 37 Brno, Czech Republic |
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Abstract: | The asymptotic behaviour and stability properties are studied for a real two‐dimensional system x′(t) = A(t)x (t) + B(t)x (θ (t)) + h (t, x (t), x (θ (t))), with a nonconstant delay t ‐ θ (t) ≥ 0. It is supposed that A,B and h are matrix functions and a vector function, respectively. The method of investigation is based on the transformation of the considered real system to one equation with complex‐valued coefficients. Stability and asymptotic properties of this equation are studied by means of a suitable Lyapunov‐Krasovskii functional. The results generalize the great part of the results of J. Kalas and L. Baráková [J. Math. Anal. Appl. 269 , No. 1, 278–300 (2002)] for two‐dimensional systems with a constant delay (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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Keywords: | Delayed differential system asymptotic behaviour stability boundedness of solutions |
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