Geodesic
The buffer phenomenon in a~mathematical model of the van der Pol self-oscillator with distributed parameters
Izvestiya. Mathematics , Tome 65 (2001) no. 3, pp. 485-501.

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We establish that a mathematical model of the distributed van der Pol self-oscillator, which is a non-linear boundary-value problem of hyperbolic type, exhibits the buffer phenomenon, which means that the system can have any given number of stable cycles if its parameters are properly chosen. 
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A. Yu. Kolesov; N. Kh. Rozov. The buffer phenomenon in a~mathematical model of the van der Pol self-oscillator with distributed parameters. Izvestiya. Mathematics , Tome 65 (2001) no. 3, pp. 485-501. http://geodesic.mathdoc.fr/item/IM2_2001_65_3_a3/

[1] Kolesov A. Yu., Kolesov Yu. S., “Bifurkatsiya avtokolebanii singulyarno vozmuschennogo volnovogo uravneniya”, DAN SSSR, 315:12 (1990), 281–283 | Zbl

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

[3] Kolesov A. Yu., Rozov N. Kh., “Postroenie periodicheskikh reshenii uravneniya tipa Bussineska s pomoschyu metoda kvazinormalnykh form”, Fundament. i prikl. matem., 1:1 (1995), 207–220 | MR | Zbl

[4] Kolesov A. Yu., “Suschestvovanie schetnogo chisla ustoichivykh tsiklov v sredakh s dispersiei”, Izv. RAN. Ser. matem., 59:3 (1995), 141–158 | MR | Zbl

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

[6] Kambulov V. F., Kolesov A. Yu., “O yavlenii bufernosti v odnoi rezonansnoi giperbolicheskoi kraevoi zadache iz radiofiziki”, Matem. sb., 186:7 (1995), 77–96 | MR | Zbl

[7] Kambulov V. F., Kolesov A. Yu., “Ob odnom modelnom giperbolicheskom uravnenii, voznikayuschem v radiofizike”, Matem. modelirovanie, 8:1 (1996), 93–102 | MR | Zbl

[8] Kambulov V. F., Kolesov A. Yu., “O spetsifike generiruemykh kolebanii v $\operatorname{RCLG}$-avtogeneratore s malym zatukhaniem v tsepi obratnoi svyazi”, Radiotekhnika i elektronika, 42:8 (1997), 1019–1024 | MR

[9] Kambulov V. F., Kolesov A. Yu., “O yavlenii bufernosti v dlinnoi linii s tunnelnym diodom”, Dokl. RAN, 355:8 (1997), 744–746 | MR | Zbl

[10] Kambulov V. F., Kolesov A. Yu., Rozov N. Kh., “Teoreticheskii i eksperimentalnyi analiz fenomena bufernosti v dlinnoi linii s tunnelnym diodom”, Differents. uravneniya, 33:5 (1997), 638–645 | MR | Zbl

[11] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR

[12] Kolesov Yu. S., “Bifurkatsiya invariantnykh torov parabolicheskikh sistem s maloi diffuziei”, Matem. sb., 184:3 (1993), 121–136 | MR | Zbl

[13] Kolesov A. Yu., “Asimptotika i ustoichivost nelineinykh parametricheskikh kolebanii singulyarno vozmuschennogo telegrafnogo uravneniya”, Matem. sb., 186:10 (1995), 57–72 | MR | Zbl

[14] Andronov A. A., Vitt A. A., Khaikin S. E., Teoriya kolebanii, Fizmatgiz, M., 1959

[15] Mischenko E. F., Rozov N. Kh., Differentsialnye uravneniya s malym parametrom i relaksatsionnye kolebaniya, Nauka, M., 1995

[16] Kolesov Yu. S., “Matematicheskaya teoriya $RC$-generatorov s raspredelennymi parametrami v tsepi obratnoi svyazi”, Differents. uravn. i ikh primenenie, no. 2, In-t fiziki i matematiki AN Lit. SSR, Vilnyus, 1971, 3–68 | MR

[17] Kambulov V. F., “Rezonansnost kak istochnik relaksatsionnykh kolebanii v sistemakh telegrafnykh uravnenii”, Dokl. RAN, 334:5 (1994), 569–570 | MR | Zbl

[18] Kambulov V. F., “Model raspredelennogo avtogeneratora Van-der-Polya”, Radiotekhnika i elektronika, 42:9 (1997), 1121–1124

[19] Koshlyanov N. S., Gliner E. B., Smirnov M. M., Uravneniya v chastnykh proizvodnykh matematicheskoi fiziki, Vysshaya shkola, M., 1970

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

[21] Reissig R., Sansone G., Konti R., Kachestvennaya teoriya nelineinykh differentsialnykh uravnenii, Nauka, M., 1974 | MR

[22] Kolesov A. Yu., “Relaksatsionnye tsikly nelineinogo volnovogo uravneniya, gladko zavisyaschego ot parametrov”, Dokl. RAN, 341:2 (1995), 158–160 | MR | Zbl