Geodesic
Extremal dynamics of the generalized Hutchinson equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 1, pp. 76-89

Voir la notice de l'article provenant de la source Math-Net.Ru

A scalar nonlinear differential-difference equation with two delays that generalizes Hutchinson's equation is considered. The bifurcation of self-oscillations of this equation from the zero equilibrium is studied in the extremal situation when one delay is asymptotically large while the other parameters are on the order of unity. Analytical methods combined with numerical techniques are used to show that the well-known buffer phenomenon occurs in the equation in this case. This means that an arbitrary finite number of different attractors coexist in the phase space of the equation with suitably chosen parameters. 
@article{ZVMMF_2009_49_1_a4,
     author = {S. D. Glyzin and A. Yu. Kolesov and N. Kh. Rozov},
     title = {Extremal dynamics of the generalized {Hutchinson} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {76--89},
     publisher = {mathdoc},
     volume = {49},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a4/}
}
TY  - JOUR
AU  - S. D. Glyzin
AU  - A. Yu. Kolesov
AU  - N. Kh. Rozov
TI  - Extremal dynamics of the generalized Hutchinson equation
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 76
EP  - 89
VL  - 49
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a4/
LA  - ru
ID  - ZVMMF_2009_49_1_a4
ER  - 
%0 Journal Article
%A S. D. Glyzin
%A A. Yu. Kolesov
%A N. Kh. Rozov
%T Extremal dynamics of the generalized Hutchinson equation
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 76-89
%V 49
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a4/
%G ru
%F ZVMMF_2009_49_1_a4
S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Extremal dynamics of the generalized Hutchinson equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 1, pp. 76-89. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a4/