Geodesic
Soft Loss of Stability in an Ocean Circulation Box Model with Turbulent Fluxes
Informatics and Automation, Analysis and singularities. Part 2, Tome 259 (2007), pp. 10-19.

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

For a 2D system of ordinary differential equations that gives a qualitative description of the thermohaline circulation in the ocean, we prove the existence of a limit cycle for a large class of transfer functions. We show that this cycle arises in the system as a result of the soft loss of stability of a steady state when a step transfer function is smoothed by functions from the above-mentioned class. 
@article{TRSPY_2007_259_a1,
     author = {A. A. Davydov and N. B. Melnikov},
     title = {Soft {Loss} of {Stability} in an {Ocean} {Circulation} {Box} {Model} with {Turbulent} {Fluxes}},
     journal = {Informatics and Automation},
     pages = {10--19},
     publisher = {mathdoc},
     volume = {259},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2007_259_a1/}
}
TY  - JOUR
AU  - A. A. Davydov
AU  - N. B. Melnikov
TI  - Soft Loss of Stability in an Ocean Circulation Box Model with Turbulent Fluxes
JO  - Informatics and Automation
PY  - 2007
SP  - 10
EP  - 19
VL  - 259
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2007_259_a1/
LA  - ru
ID  - TRSPY_2007_259_a1
ER  - 
%0 Journal Article
%A A. A. Davydov
%A N. B. Melnikov
%T Soft Loss of Stability in an Ocean Circulation Box Model with Turbulent Fluxes
%J Informatics and Automation
%D 2007
%P 10-19
%V 259
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2007_259_a1/
%G ru
%F TRSPY_2007_259_a1
A. A. Davydov; N. B. Melnikov. Soft Loss of Stability in an Ocean Circulation Box Model with Turbulent Fluxes. Informatics and Automation, Analysis and singularities. Part 2, Tome 259 (2007), pp. 10-19. http://geodesic.mathdoc.fr/item/TRSPY_2007_259_a1/

[1] Alekseev V. V., Gusev A. M., “Svobodnaya konvektsiya v geofizicheskikh protsessakh”, UFN, 141:2 (1983), 311–342

[2] Taylor F. W., Elementary climate physics, Oxford Univ. Press, Oxford, 2005

[3] Rahmstorf S., Crucifix M., Ganopolski A., Goosse H., Kamenkovich I., Knutti R., Lohmann G., Marsh R., Mysak L. A., Wang Z., Weaver A. J., “Thermohaline circulation hysteresis: A model intercomparison”, Geophys. Res. Lett., 32 (2005), L23605 | DOI

[4] Keller K., McInerney D., “The dynamics of learning about a climate threshold”, Clim. Dyn., 2007 (to appear)

[5] Titz S., Kuhlbrodt T., Feudel U., “Homoclinic bifurcation in an ocean circulation box model”, Intern. J. Bifurcation and Chaos, 12:4 (2002), 869–875 | DOI

[6] Stommel H., “Thermohaline convection with two stable regimes of flow”, Tellus., 13 (1961), 224–230 | DOI

[7] Cessi P. A., “Simple box model of stochastically forced thermohaline flow”, J. Phys. Oceanogr., 24:9 (1994), 1911–1920 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[8] Marotzke J., “Abrupt climate change and thermohaline circulation: Mechanisms and predictability”, Proc. Nat. Acad. Sci. USA, 97:4 (2000), 1347–1350 | DOI

[9] Welander P. A., “A simple heat–salt oscillator”, Dyn. Atmos. and Oceans, 6:4 (1982), 233–242 | DOI

[10] Arnold V. I., Geometricheskie metody v teorii obyknovennykh differentsialnykh uravnenii, 2-e izd., Regulyarnaya i khaoticheskaya dinamika, Izhevsk, 1999 | Zbl

[11] Filippov A. F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985 | MR

[12] Davydov A. A., Melnikov N. B., “Bifurkatsiya Andronova–Khopfa v prostykh modelyakh dvoinoi diffuzii”, UMN, 62:2 (2007), 175–176 | MR | Zbl

[13] Davydov A. A., Melnikov N. B., Existence of self-sustained oscillations in an ocean circulation box model with turbulent fluxes, Interim Rept. IR-06-049, IIASA, Laxenburg (Austria), 2006 | MR

[14] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl

[15] Arnold V. I., Obyknovennye differentsialnye uravneniya, Nauka, M., 1984 | MR