Displaying similar documents to “Convergence to equilibria in a differential equation with small delay”

Convergence to equilibria in a differential equation with small delay

Mihály Pituk (2002)

Mathematica Bohemica

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Consider the delay differential equation x ˙ ( t ) = g ( x ( t ) , x ( t - r ) ) , ( 1 ) where r > 0 is a constant and g ℝ 2 → ℝ is Lipschitzian. It is shown that if  r is small, then the solutions of (1) have the same convergence properties as the solutions of the ordinary differential equation obtained from (1) by ignoring the delay.

On time transformations for differential equations with state-dependent delay

Alexander Rezounenko (2014)

Open Mathematics

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Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.

Characterization of shadowing for linear autonomous delay differential equations

Mihály Pituk, John Ioannis Stavroulakis (2025)

Czechoslovak Mathematical Journal

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A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear autonomous delay differential equation is shadowable if and only if its characteristic equation has no root on the imaginary axis. The proof is based on the decomposition theory of linear delay differential equations.