Geodesic
The buffering phenomenon in a resonance hyperbolic boundary-value problem in radiophysics
Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 1003-1021 
V. F. Kambulov; A. Yu. Kolesov. The buffering phenomenon in a resonance hyperbolic boundary-value problem in radiophysics. Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 1003-1021. http://geodesic.mathdoc.fr/item/SM_1995_186_7_a5/
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     title = {The buffering phenomenon in a~resonance hyperbolic boundary-value problem in radiophysics},
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Voir la notice de l'article provenant de la source Math-Net.Ru

By the buffering phenomenon we mean the existence of sufficiently many stable cycles in a system of differential equations with distributed coefficients. In systems of parabolic reaction-diffusion equations this interesting phenomenon was first discovered by numerical methods in [1] in which a problem in ecology was studied. It was then explained theoretically in [2] and [3]. The buffering phenomenon is of current interest, for example, in connection with the modelling of memory processes and the creation of memory cells [4]. It is therefore interesting to find simple radiophysical devices with this property. In the present paper we consider a mathematical model of such a device (an $\operatorname{RCLG}$-oscillator) and, with the aid of a suitable modification of the methods developed in [5], we study the problem of existence and stability of its periodic solutions.

[1] Zakharov A. A., Kolesov Yu. S., “Prostranstvenno neodnorodnye rezhimy v zadache khischnik–zhertva”, Nelineinye kolebaniya i ekologiya, Yaroslavl, 1984, 3–15 | MR

[2] Kolesov A. Yu., “Suschestvovanie asimptoticheski bolshogo chisla ustoichivykh beguschikh voln v odnoi trekhmernoi sisteme parabolicheskikh uravnenii”, Metody kachestvennoi teorii differentsialnykh uravnenii, Mezhvuz. sb., Gorkovskii universitet, 1986, 57–66 | MR | Zbl

[3] Kolesov A. Yu., “Teoreticheskoe ob'yasnenie yavleniya diffuzionnoi bufernosti”, Modelirovanie dinamiki populyatsii, N. Novgorod, 1990, 35–38 | MR

[4] Utkin G. M., “Metod medlenno menyayuschikhsya stoyachikh voln v teorii raspredelennykh avtogeneratorov”, Radiotekhnika i elektronika, 2 (1969), 267–276

[5] Kolesov A. Yu., “Ustoichivost avtokolebanii telegrafnogo uravneniya, bifurtsiruyuschikh iz sostoyaniya ravnovesiya”, Matem. zametki, 51:2 (1992), 59–65 | MR | Zbl

[6] Kambulov V. F., “Raschet avtokolebanii v $\operatorname {RCLG}$-generatorakh s raspredelennymi parametrami v tsepi obratnoi svyazi”, Issledovaniya po ustoichivosti i teorii kolebanii, Yaroslavl, 1976, 86–89

[7] Kulikov A. N., “Issledovanie odnoi kraevoi zadachi, voznikayuschei v radiofizike”, Issledovaniya po ustoichivosti i teorii kolebanii, Yaroslavl, 1976, 67–85

[8] Koshlyakov N. S., Gliner E. B., Smirnov M. M., Uravneniya v chastnykh proizvodnykh matematicheskoi fiziki, Vysshaya shkola, M., 1970 | Zbl

[9] Kolesov Yu. S., Shvitra D. I., Avtokolebaniya v sistemakh s zapazdyvaniem, Moklas, Vilnyus, 1979 | Zbl

[10] Kolesov Yu. S., Maiorov V. V., “Novyi metod issledovaniya ustoichivosti reshenii lineinykh differentsialnykh uravnenii s blizkimi k postoyannym pochti periodicheskimi koeffitsientami”, Differents. uravn., 10:10 (1974), 1778–1788 | MR | Zbl

[11] Kolesov A. Yu., “Parametricheskie kolebaniya reshenii telegrafnogo uravneniya s umerenno maloi diffuziei”, Sib. matem. zhurn., 33:6 (1992), 79–86 | MR | Zbl

[12] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1968 | MR | Zbl

[13] Kolesov Yu. S., “Ob ustoichivosti reshenii lineinykh differentsialnykh uravnenii parabolicheskogo tipa s pochti periodicheskimi koeffitsientami”, Tr. MMO, 36, URSS, M., 1978, 3–27 | MR | Zbl