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Uspekhi Mat. Nauk, 2008, Volume 63, Issue 5(383), Pages 3–72 (Mi umn9237)  

This article is cited in 45 scientific papers (total in 46 papers)

Asymptotic analysis of autoresonance models

L. A. Kalyakin

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: In recent decades new problems have arisen in oscillation theory which are related to the investigation of a physical phenomenon known as autoresonance. This paper presents a survey of results on the asymptotic analysis of such problems. Systems of differential equations corresponding to non-linear non-autonomous oscillators with variable excitation frequency are considered. For their solution asymptotic formulae are constructed with respect to a small parameter or with respect to an independent variable.


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English version:
Russian Mathematical Surveys, 2008, 63:5, 791–857

Bibliographic databases:

Document Type: Article
UDC: 517.956
MSC: Primary 70K30, 34C15, 34E05; Secondary 34E10, 41A60, 78M35
Received: 10.05.2008

Citation: L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Uspekhi Mat. Nauk, 63:5(383) (2008), 3–72; Russian Math. Surveys, 63:5 (2008), 791–857

Citation in format AMSBIB
\by L.~A.~Kalyakin
\paper Asymptotic analysis of autoresonance models
\jour Uspekhi Mat. Nauk
\yr 2008
\vol 63
\issue 5(383)
\pages 3--72
\jour Russian Math. Surveys
\yr 2008
\vol 63
\issue 5
\pages 791--857

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    This publication is cited in the following articles:
    1. L. A. Kalyakin, “Metod usredneniya v zadachakh ob asimptotike na beskonechnosti”, Ufimsk. matem. zhurn., 1:2 (2009), 29–52  mathnet  zmath  elib
    2. Shamsutdinov M.A., Kalyakin L.A., Sukhonosov A.L., Kharisov A.T., “Avtorezonansnyi metod upravleniya slaborelyativistskoi dinamikoi domennoi stenki”, Vestn. Chelyabinskogo gos. un-ta, 2009, no. 25, 5–12  elib
    3. Makarov D.V., Sosedko E.V., Uleysky M.Yu., “Frequency-modulated ratchet with autoresonance”, Eur. Phys. J. B, 73:4 (2010), 571–579  crossref  adsnasa  isi  elib  scopus
    4. Tarkhanov N., Glebov S., Kiselev O., “Autoresonance in a dissipative system”, J. Phys. A, 43:21 (2010), 215203, 16 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. A. E. Elbert, A. R. Danilin, “Avtofazirovka solitonov s optimizatsiei”, Tr. IMM UrO RAN, 16, no. 2, 2010, 288–296  mathnet  elib
    6. Shamsutdinov M.A., Kalyakin L.A., Kharisov A.T., “Upravlenie nelineinoi dinamikoi namagnichennosti maloi ferromagnitnoi chastitsy”, Izv. RAN. Ser. fiz., 74:10 (2010), 1444–1446  zmath  elib
    7. Shamsutdinov M.A., Kalyakin L.A., Sukhonosov A.L., Kharisov A.T., “Controlling quasi-relativistic dynamics of domain walls in the regime of self-phasing”, Physics of Metals and Metallography, 110:5 (2010), 430–441  crossref  adsnasa  isi  elib  scopus
    8. Shamsutdinov M.A., Kalyakin L.A., Kharisov A.T., “Autoresonance in a ferromagnetic film”, Technical Physics, 55:6 (2010), 860–865  crossref  adsnasa  isi  elib  elib  scopus
    9. L. A. Kalyakin, “Analysis of a synchronization model in an anisochronous system”, Comput. Math. Math. Phys., 50:8 (2010), 1338–1349  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    10. L. A. Kalyakin, O. A. Sultanov, M. A. Shamsutdinov, “Asymptotic analysis of a model of nuclear magnetic autoresonance”, Theoret. and Math. Phys., 167:3 (2011), 762–771  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    11. Ermakov A.V., Hinch B.J., “Trajectory compensation in an autoresonant trap mass spectrometer”, J. Mass. Spectrom., 46:7 (2011), 672–676  crossref  isi
    12. Batalov S., Shagalov A., “Control of solitons”, Phys. Rev. E, 84:1 (2011), 016603, 7 pp.  crossref  mathscinet  adsnasa  isi  elib  scopus
    13. Kharisov A.T., Kalyakin L.A., Shamsutdinov M.A., “Autoresonance excitation of nonlinear oscillations of magnetization and domain walls in ferromagnets”, Trends in magnetism, Solid State Phenomena, 168-169, 2011, 77–80  crossref  isi  scopus
    14. Nazarov V.N., Kalyakin L.A., Shamsutdinov M.A., “Autoresonance parametric excitation of the magnetic breather in a uniaxial ferromagnet”, Trends in magnetism, Solid State Phenomena, 168-169, 2011, 81–84  crossref  isi  scopus
    15. L. A. Kalyakin, “Stability of Nondissipative Systems under Persistent Random Perturbations”, Math. Notes, 92:1 (2012), 136–139  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    16. R. N. Garifullin, “Autoresonance excitation of a soliton of the nonlinear Schrödinger equation”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 59–63  mathnet  crossref  isi  elib
    17. O. A. Sultanov, “Ustoichivost modelei avtorezonansa pri postoyanno deistvuyuschikh vozmuscheniyakh”, Tr. IMM UrO RAN, 18, no. 2, 2012, 254–264  mathnet  elib
    18. L. A. Kalyakin, “Ustoichivost nedissipativnykh sistem otnositelno sluchainykh vozmuschenii, malykh v srednem”, Tr. IMM UrO RAN, 19, no. 2, 2013, 170–178  mathnet  mathscinet  elib
    19. A. Kovaleva, L.I. Manevitch, “Limiting phase trajectories and emergence of autoresonance in nonlinear oscillators”, Phys. Rev. E, 88:2 (2013), 024901  crossref  mathscinet  adsnasa  isi  scopus
    20. V. P. Milant'ev, “Cyclotron autoresonance—50 years since its discovery”, Phys. Usp., 56:8 (2013), 823–832  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    21. O. A. Sultanov, “Ustoichivost modelei avtorezonansa otnositelno vozmuschenii, ogranichennykh v srednem”, Tr. IMM UrO RAN, 19, no. 3, 2013, 274–283  mathnet  mathscinet  elib
    22. Kalyakin L.A., Sultanov O.A., “Stability of Autoresonance Models”, Differ. Equ., 49:3 (2013), 267–281  crossref  mathscinet  zmath  isi  elib  scopus
    23. O. A. Sultanov, “Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations”, Comput. Math. Math. Phys., 54:1 (2014), 59–73  mathnet  crossref  crossref  isi  elib  elib
    24. Oleg Kiselev, Nikolai Tarkhanov, “Scattering of trajectories at a separatrix under autoresonance”, J. Math. Phys, 55:6 (2014), 063502  crossref  mathscinet  zmath  isi  scopus
    25. L. A. Kalyakin, “Phantom asymptotic solutions”, Ufa Math. J., 6:2 (2014), 44–65  mathnet  crossref  elib
    26. L. A. Kalyakin, “Synchronization in a nonisochronous nonautonomous system”, Theoret. and Math. Phys., 181:2 (2014), 1339–1348  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    27. Kalyakin L.A., “Lyapunov Functions in Barriers For Parabolic Equations and in Stability Problems With Respect To “White Noise””, Russ. J. Math. Phys., 21:4 (2014), 472–483  crossref  mathscinet  zmath  isi  scopus
    28. S.H.. Sandilo, W.T.. van Horssen, “On a cascade of autoresonances in an elevator cable system”, Nonlinear Dyn, 2015  crossref  isi  scopus
    29. L. A. Kalyakin, “Stability of equilibrium with respect to a white noise”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 68–77  mathnet  crossref  mathscinet  elib
    30. O. M. Kiselev, “Asymptotics of an autoresonance soliton”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 75–84  mathnet  crossref  mathscinet  isi  elib
    31. O. A. Sultanov, “Stability of capture into parametric autoresonance”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 156–167  mathnet  crossref  mathscinet  elib
    32. O. A. Sultanov, “Stability of autoresonance in dissipative systems”, Ufa Math. J., 7:1 (2015), 58–69  mathnet  crossref  isi  elib
    33. L. A. Kalyakin, “Lyapunov Functions in Justification Theorems for Asymptotics”, Math. Notes, 98:5 (2015), 752–764  mathnet  crossref  crossref  mathscinet  isi  elib
    34. Kalyakin L.A., “Stability of the autoresonance in a dissipative system”, Russ. J. Math. Phys., 23:1 (2016), 77–87  crossref  mathscinet  zmath  isi  elib  scopus
    35. Kayumov I.R., Shikhovtseva E.S., Nazarov V.N., “The Dynamics of 360 Degrees Domain Walls in Weak Ferromagnets in Autoresonant Mode”, Lett. Mater., 6:3 (2016), 173–178  crossref  isi  scopus
    36. L. A. Kalyakin, “Asymptotic analysis of the model of gyromagnetic autoresonance”, Comput. Math. Math. Phys., 57:2 (2017), 281–296  mathnet  crossref  crossref  isi  elib
    37. L. A. Kalyakin, “Adiabatic approximation for a Model of Cyclotron Motion”, Math. Notes, 101:5 (2017), 850–862  mathnet  crossref  crossref  mathscinet  isi  elib
    38. L. A. Kalyakin, “Uravnenie Penleve-II kak model rezonansnogo vzaimodeistviya ostsillyatorov”, Tr. IMM UrO RAN, 23, no. 2, 2017, 104–116  mathnet  crossref  elib
    39. L. A. Kalyakin, “Adiabatic approximation in a resonance capture problem”, Ufa Math. J., 9:3 (2017), 61–75  mathnet  crossref  isi  elib
    40. Sultanov O., “Random Perturbations of Parametric Autoresonance”, Nonlinear Dyn., 89:4 (2017), 2785–2793  crossref  mathscinet  zmath  isi  scopus
    41. Kiselev O.M., “Asymptotic Behaviour of Measure For Captured Trajectories Into Parametric Autoresonance”, Nonlinear Dyn., 91:3 (2018), 1977–1983  crossref  zmath  isi  scopus
    42. Manevitch L.I., Kovaleva A., Smirnov V., Starosvetsky Yu., “Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures Introduction”: Manevitch, LI Kovaleva, A Smirnov, V Starosvetsky, Y, Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures, Foundations of Engineering Mechanics, Springer-Verlag Berlin, 2018, XV–XXII  isi
    43. Manevitch L.I., Kovaleva A., Smirnov V., Starosvetsky Yu., “Limiting Phase Trajectories and the Emergence of Autoresonance in Anharmonic Oscillators”: Manevitch, LI Kovaleva, A Smirnov, V Starosvetsky, Y, Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures, Foundations of Engineering Mechanics, Springer-Verlag Berlin, 2018, 195–223  crossref  isi  scopus
    44. Nazarov V.N., Ekomasov E.G., “Autoresonance Control Model of Nonlinear Dynamics of Magnetization in a Three-Layer Antiferromagnetic Structure in the Presence of Attenuation”, Lett. Mater., 8:2 (2018), 158–164  crossref  isi  scopus
    45. L. A. Kalyakin, “Resonance capture in a system of two oscillators near equilibrium”, Theoret. and Math. Phys., 194:3 (2018), 331–346  mathnet  crossref  crossref  isi  elib
    46. L. A. Kalyakin, “Capture and holding of resonance far from equilibrium”, Ufa Math. J., 10:4 (2018), 64–76  mathnet  crossref  isi
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