Geodesic
Stability of the Simplest Periodic Solutions in the Stuart–Landau Equation with Large Delay
Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 136-141 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study the local dynamics of the Stuart–Landau equation with large delay in the neibourhood of periodic solutions. We find sufficient conditions of instability of periodic solutions and sufficient conditions of their stability.
Keywords: Stuart—Landau equation, small parameter, large delay, stability, periodic solution. 
@article{MAIS_2012_19_3_a9,
     author = {A. A. Kashchenko},
     title = {Stability of the {Simplest} {Periodic} {Solutions} in the {Stuart{\textendash}Landau} {Equation} with {Large} {Delay}},
     journal = {Modelirovanie i analiz informacionnyh sistem},
     pages = {136--141},
     year = {2012},
     volume = {19},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a9/}
}
TY  - JOUR
AU  - A. A. Kashchenko
TI  - Stability of the Simplest Periodic Solutions in the Stuart–Landau Equation with Large Delay
JO  - Modelirovanie i analiz informacionnyh sistem
PY  - 2012
SP  - 136
EP  - 141
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a9/
LA  - ru
ID  - MAIS_2012_19_3_a9
ER  - 
%0 Journal Article
%A A. A. Kashchenko
%T Stability of the Simplest Periodic Solutions in the Stuart–Landau Equation with Large Delay
%J Modelirovanie i analiz informacionnyh sistem
%D 2012
%P 136-141
%V 19
%N 3
%U http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a9/
%G ru
%F MAIS_2012_19_3_a9
A. A. Kashchenko. Stability of the Simplest Periodic Solutions in the Stuart–Landau Equation with Large Delay. Modelirovanie i analiz informacionnyh sistem, Tome 19 (2012) no. 3, pp. 136-141. http://geodesic.mathdoc.fr/item/MAIS_2012_19_3_a9/

[1] G. L. Johnston, D. V. Ramana Reddy, A. Sen, “Time delay effects on coupled limit cycle oscillators at Hopf bifurcation”, Physica D, 129 (1999), 15–34 | DOI | MR | Zbl

[2] G. L. Johnston, D. V. Ramana Reddy, A. Sen, “Dynamics of a limit cycle oscillator under time delayed linear and nonlinear feedbacks”, Physica D, 144 (2000), 335–357 | DOI | MR | Zbl

[3] I. S. Kaschenko, “Normalizatsiya v sisteme s dvumya blizkimi bolshimi zapazdyvaniyami”, Nelineinaya Dinamika, 6:1 (2010), 169–180 | MR

[4] I. S. Kaschenko, “Dinamika uravneniya s bolshim koeffitsientom zapazdyvayuschego upravleniya”, DAN, 437:6 (2011), 743–747

[5] I. S. Kaschenko, “Asimptoticheskoe issledovanie korporativnoi dinamiki sistem uravnenii, svyazannykh cherez zapazdyvayuschee upravlenie”, DAN, 443:1 (2012), 9–13

[6] J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer, 1996 | MR