Geodesic
The buffer phenomenon in ring-like chains of unidirectionally connected generators
Izvestiya. Mathematics , Tome 78 (2014) no. 4, pp. 708-743

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

We introduce a new object, namely, a system of ordinary differential equations which is a mathematical model of a ring-like chain of unidirectionally connected RCL-generators. To study periodic solutions of travelling wave type of this system, some special tricks are used which reduce the existence and stability problems for cycles to the investigation of auxiliary delay equations. Using this approach, we establish that the number of stable travelling waves simultaneously existing in the chain increases unboundedly as the number of links of the chain increases, that is, the well-known buffer phenomenon occurs.
Keywords: chain of unidirectionally connected generators, travelling wave, asymptotic behaviour, stability, buffer phenomenon. 
@article{IM2_2014_78_4_a2,
     author = {S. D. Glyzin and A. Yu. Kolesov and N. Kh. Rozov},
     title = {The buffer phenomenon in ring-like chains of unidirectionally connected generators},
     journal = {Izvestiya. Mathematics },
     pages = {708--743},
     publisher = {mathdoc},
     volume = {78},
     number = {4},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2014_78_4_a2/}
}
TY  - JOUR
AU  - S. D. Glyzin
AU  - A. Yu. Kolesov
AU  - N. Kh. Rozov
TI  - The buffer phenomenon in ring-like chains of unidirectionally connected generators
JO  - Izvestiya. Mathematics 
PY  - 2014
SP  - 708
EP  - 743
VL  - 78
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2014_78_4_a2/
LA  - en
ID  - IM2_2014_78_4_a2
ER  - 
%0 Journal Article
%A S. D. Glyzin
%A A. Yu. Kolesov
%A N. Kh. Rozov
%T The buffer phenomenon in ring-like chains of unidirectionally connected generators
%J Izvestiya. Mathematics 
%D 2014
%P 708-743
%V 78
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2014_78_4_a2/
%G en
%F IM2_2014_78_4_a2
S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. The buffer phenomenon in ring-like chains of unidirectionally connected generators. Izvestiya. Mathematics , Tome 78 (2014) no. 4, pp. 708-743. http://geodesic.mathdoc.fr/item/IM2_2014_78_4_a2/