Geodesic
Buffering effect in continuous chains of unidirectionally coupled generators
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 2, pp. 254-275

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We propose a mathematical model of a continuous annular chain of unidirectionally coupled generators given by some nonlinear advection-type hyperbolic boundary value problem. Such problems are constructed by a limit transition from annular chains of unidirectionally coupled ordinary differential equations with an unbounded increase in the number of links. We find that a certain buffering phenomenon is realized in our boundary value problem. Namely, we show that any preassigned finite number of stable periodic motions of the traveling-wave type can coexist in the model.
Keywords: continuous chain of unidirectionally coupled generators, buffering, traveling wave, asymptotic form, stability. 
@article{TMF_2014_181_2_a1,
     author = {S. D. Glyzin and A. Yu. Kolesov and N. Kh. Rozov},
     title = {Buffering effect in continuous chains of unidirectionally coupled generators},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {254--275},
     publisher = {mathdoc},
     volume = {181},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a1/}
}
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S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Buffering effect in continuous chains of unidirectionally coupled generators. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 2, pp. 254-275. http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a1/