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Asymptotic behavior of solutions of third order delay differential equations

Mariella Cecchi, Zuzana Došlá (1997)

Archivum Mathematicum

We give an equivalence criterion on property A and property B for delay third order linear differential equations. We also give comparison results on properties A and B between linear and nonlinear equations, whereby we only suppose that nonlinearity has superlinear growth near infinity.

Coordinate description of analytic relations

František Neuman (2006)

Mathematica Bohemica

In this paper we present an algebraic approach that describes the structure of analytic objects in a unified manner in the case when their transformations satisfy certain conditions of categorical character. We demonstrate this approach on examples of functional, differential, and functional differential equations.

Decomposition of a second-order linear time-varying differential system as the series connection of two first order commutative pairs

Mehmet Emir Koksal (2016)

Open Mathematics

Necessary and sufficiently conditions are derived for the decomposition of a second order linear time- varying system into two cascade connected commutative first order linear time-varying subsystems. The explicit formulas describing these subsystems are presented. It is shown that a very small class of systems satisfies the stated conditions. The results are well verified by simulations. It is also shown that its cascade synthesis is less sensitive to numerical errors than the direct simulation...

Decoupling normalizing transformations and local stabilization of nonlinear systems

S. Nikitin (1996)

Mathematica Bohemica

The existence of the normalizing transformation completely decoupling the stable dynamic from the center manifold dynamic is proved. A numerical procedure for the calculation of the asymptotic series for the decoupling normalizing transformation is proposed. The developed method is especially important for the perturbation theory of center manifold and, in particular, for the local stabilization theory. In the paper some sufficient conditions for local stabilization are given.

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