Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability

Josef Kalas; Josef Rebenda

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Displaying similar documents to “Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability”

Asymptotic properties of an unstable two-dimensional differential system with delay

Josef Kalas (2006)

Mathematica Bohemica

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The asymptotic behaviour of the solutions is studied for a real unstable two-dimensional system $x^{'} (t) = 𝖠 (t) x (t) + 𝖡 (t) x (t - r) + h (t, x (t), x (t - r))$ , where $r > 0$ is a constant delay. It is supposed that $𝖠$ , $𝖡$ and $h$ are matrix functions and a vector function, respectively. Our results complement those of Kalas [Nonlinear Anal. 62(2) (2005), 207–224], where the conditions for the existence of bounded solutions or solutions tending to the origin as $t \to \infty$ are given. The method of investigation is based on the transformation of the real system considered...

Asymptotic estimation of the convergence of solutions of the equation $\dot{x} (t) = b (t) x (t - τ (t))$

Josef Diblík, Denis Khusainov (2001)

Archivum Mathematicum

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The main result of the present paper is obtaining new inequalities for solutions of scalar equation $\dot{x} (t) = b (t) x (t - τ (t))$ . Except this the interval of transient process is computed, i.e. the time is estimated, during which the given solution $x (t)$ reaches an $ε$ - neighbourhood of origin and remains in it.

Displaying similar documents to “Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability”

Asymptotic properties of an unstable two-dimensional differential system with delay

Asymptotic estimation of the convergence of solutions of the equation x ˙ ( t ) = b ( t ) x ( t - τ ( t ) )

Asymptotic estimation of the convergence of solutions of the equation $\dot{x} (t) = b (t) x (t - τ (t))$