A method for detection of Hopf bifurcation points

A. S. Bratus'   ; A. L. Khalin

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 42 (2002) no. 3, pp. 336-350

Bibliographie

[1] Bautin N. N., Leontovich E. A., Metody i priemy kachestvennogo issledovaniya dinamicheskikh sistem na ploskosti, Nauka, M., 1976 | MR

[2] Kuznesov Y. A., Elements of applied bifurcation theory, Appl. Math. Sci., Springer, New York, 1995 | MR

[3] Marsden Dzh., Mak-Kraken M., Bifurkatsiya rozhdeniya tsikla i ee prilozheniya, Mir, M., 1980 | MR | Zbl

[4] Khessard B., Kazarinov N., Ven I., Teoriya i prilozheniya bifurkatsii rozhdeniya tsikla, Mir, M., 1985 | MR

[5] Krasnoselskii M. A., “O rozhdenii avtokolebanii iz sostoyaniya ravnovesiya”, Avtomatika i telemekhan., 1973, no. 1, 182–184

[6] Yumagulov M. G., “Metod funktsionalizatsii parametra v zadache priblizhennogo rascheta malykh avtokolebatelnykh rezhimov”, Avtomatika i telemekhan., 1988, no. 10, 76–84 | MR | Zbl

[7] Krasnoselskii M. A., Kuznetsov N. A., Yumagulov M. G., “Funktsionalizatsiya parametra i asimptotika tsiklov v bifurkatsii Khopfa”, Avtomatika i telemekhan., 1996, no. 11, 22–28 | MR

[8] Magnitskii N. A., “Bifurkatsiya Khopfa v sisteme Resslera”, Diferents. ur-niya, 31:3 (1995), 538–541 | MR

[9] Khibnik A. M., Shnol E. E., Programmy dlya kachestvennogo issledovaniya differentsialnykh uravnenii. Informatsionnye materialy, ONTI NTsBI AN SSSR, Puschino, 1982

[10] Pheinbolt W. C., Roose D., Seydel R., “Aspects of continuation software”, Continuation and Bifurcation: Numer. Techn. and Appl., Kluwer Acad. Press, Dordrecht etc., 1990, 261–268 | MR

[11] Rosendorf P., Orsag J., Schreiber I., Marec M., “Interactive system for studies in nonlinear dynamics”, Continuation and Bifurcation: Numer. Techn. and Appl., Kluwer Acad. Press., Dordrecht etc., 1990, 269–282

[12] Khibnik A. J., “LINLBF: A program for continuation and bifurcation analysis of equlibia up to codimention three”, Continuation and Bifurcation: Numer. Techn. and Appl., Kluwer Acad. Press, Dordrecht etc., 1990, 283–296 | MR

[13] Moore G., Garrat T. J., Spence A., “The numerical detection of Hopf bifurcation points”, Continuation and Bifurcation: Numer. Techn. and Appl., Kluwer Acad. Press, Dordrecht etc., 1990, 227–246 | MR

[14] Kato T., Teoriya vozmuscheniya lineinykh operatorov, Mir, M., 1972 | Zbl

[15] Postnikov M. M., Gladkie mnogoobraziya, Nauka, M., 1987 | MR | Zbl

[16] Tom R., Levin G., “Osobennosti differentsiruemykh otobrazhenii”, Osobennosti differentsiruemykh otobrazhenii, Mir, M., 1968, 9–101 | MR

[17] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989 | MR

[18] Lyusternik L. A., Sobolev V. I., Kratkii kurs funktsionalnogo analiza, Vyssh. shkola, M., 1982 | MR | Zbl

[19] Bokhner S., Martin U. T., Funktsii mnogikh kompleksnykh peremennykh, Izd-vo inostr. lit., M., 1951

[20] Khorn R., Dzhonson I., Matrichnyi analiz, Mir, M., 1989 | MR

[21] Erve M., Funktsii mnogikh kompleksnykh peremennykh, Mir, M., 1965 | MR

[22] Ortega Dzh., Reinbolt V., Iteratsionnye metody resheniya nelineinykh uravnenii so mnogimi peremennymi, Mir, M., 1985

[23] Dennis Dzh., Shnabel R., Chislennye metody bezuslovnoi optimizatsii i reshenie nelineinykh uravnenii, Mir, M., 1988 | MR | Zbl

[24] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1988 | MR

[25] Gill F., Myurrei U., Rait M., Prakticheskaya optimizatsiya, Mir, M., 1985 | MR

[26] Smith B. T., Boyle J. M., Dongarra J. J. et al., Matrix eigensystem routines – EISPACK guide, Lect. Notes in Computer Sci., 6, Springer, Berlin, 1976 | MR | Zbl

[27] Arnold V. I., Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978 | MR

[28] Errousmit D., Pleis K., Obyknovennye differentsialnye uravneniya, Mir, M., 1986

[29] Rakitskii Yu. V., Ustinov S. M., Chernorutskii I. G., Chislennye metody resheniya zhestkikh sistem, Nauka, M., 1979 | MR

[30] Dzh. Kholl, Dzh. Uatt (red.), Sovremennye chislennye metody resheniya obyknovennykh differentsialnykh uravnenii, Mir, M., 1979

[31] Vazykin A. D., Matematicheskaya biofizika vzaimodeistvuyuschikh populyatsii, Nauka, M., 1985 | MR

[32] Garel D., Garel O., Kolebatelnye khimicheskie reaktsii, Mir, M., 1986