Abstract:
It is assumed that the equilibrium state of the relaxation system
ε˙x=f(x,y),˙y=g(x,y,μ),
where x∈Rn and y∈R, passes generically through a point of discontinuity as μ varies. Under this condition stable duck cycles and cycles arising in a neighborhood of the equilibrium state are constructed.
Citation:
A. Yu. Kolesov, E. F. Mishchenko, “The Pontryagin delay phenomenon and stable ducktrajectories for multidimensional relaxation systems with one slow variable”, Math. USSR-Sb., 70:1 (1991), 1–10
\Bibitem{KolMis90}
\by A.~Yu.~Kolesov, E.~F.~Mishchenko
\paper The Pontryagin delay phenomenon and stable ducktrajectories for multidimensional relaxation systems with one slow variable
\jour Math. USSR-Sb.
\yr 1991
\vol 70
\issue 1
\pages 1--10
\mathnet{http://mi.mathnet.ru/eng/sm1190}
\crossref{https://doi.org/10.1070/SM1991v070n01ABEH002117}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1055975}
\zmath{https://zbmath.org/?q=an:0731.34028}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1991SbMat..70....1K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1991GG78300001}
Linking options:
https://www.mathnet.ru/eng/sm1190
https://doi.org/10.1070/SM1991v070n01ABEH002117
https://www.mathnet.ru/eng/sm/v181/i5/p579
This publication is cited in the following 5 articles:
Christian Kuehn, Applied Mathematical Sciences, 191, Multiple Time Scale Dynamics, 2015, 197
N. A. Arzhanova, M. A. Prokaznikov, A. V. Prokaznikov, “Self-organization process under electrolytic formation of nanostructures in silicon-based semi-conducting systems”, Russ Microelectron, 43:6 (2014), 413
D. V. Anosov, S. M. Aseev, R. V. Gamkrelidze, S. P. Konovalov, M. S. Nikol'skii, N. Kh. Rozov, “Evgenii Frolovich Mishchenko (on the 90th anniversary of his birth)”, Russian Math. Surveys, 67:2 (2012), 385–402
A. Yu. Kolesov, N. Kh. Rozov, “The “Buridan's Ass” problem in relaxation systems with one slow variable”, Math. Notes, 65:1 (1999), 128–131
Kolesov A. Rozov N., “Cycles-Ducks of Three-Dimensional Relaxation Systems with a Fast Variable and Two Slow Variables”, Differ. Equ., 32:2 (1996), 181–185
Citation in format AMSBIB
Contact us: