Abstract
We investigate the problem of constructing asymptotic decompositions of integral manifolds of slow variables for linear and nonlinear singularly perturbed systems with delay.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yu. A. Mitrolpol’skii and V. I. Fodchuk, “On the stable integral manifolds for a class of singularly perturbed delay systems,”Ukr. Mat. Zh.,20, No. 6, 791–801 (1968).
Yu. A. Mitrolpol’skii and V. I. Fodchuk, “On the existence and stability of a bounded solution for a singularly perturbed delay system,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 3, 210–213 (1969).
V. I. Fodchuk and I. M. Cherevko, “On the theory of integral manifolds for singularly perturbed systems of differential-difference equations,”Ukr. Mat. Zh.,34, No. 6, 725–731 (1982).
A. Halanay, “An invariant surface for some linear singularly perturbed systems with time lag,”J. Differential Equations,2, No. 2, 33–46 (1966).
V. V. Strygin and V. A. Sobolev,Separation of Motions via the Method of Integral Manifolds [in Russian], Nauka, Moscow (1988).
N. V. Voropaeva and V. A. Sobolev, “A constructive method for splitting nonlinear singularly perturbed systems,”Differents. Uravn.,31, No. 4, 569–578 (1995).
I. M. Cherevko, “The splitting of linear singularly perturbed differential-difference systems,”Dopov. Nats. Akad. Nauk Ukr., No. 6, 42–45 (1997).
O. B. Lykova and Ya. S. Baris,Approximate Integral Manifolds [in Russian], Naukova Dumka, Kiev (1993).
Additional information
Chernivtsi University, Chernivtsi. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 8, pp. 1105–1111, August, 1999.
Rights and permissions
About this article
Cite this article
Cherevko, I.M. On the asymptotics of integral manifolds of singularly perturbed systems with delay. Ukr Math J 51, 1246–1254 (1999). https://doi.org/10.1007/BF02592512
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02592512