Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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Nelin. Dinam., 2012, Volume 8, Number 1, Pages 3–28 (Mi nd300)  

This article is cited in 31 scientific papers (total in 31 papers)

Towards scenarios of chaos appearance in three-dimensional maps

A. S. Gonchenko, S. V. Gonchenko, L. P. Shilnikov

Research Institute for Applied Mathematics and Cybernetics, Ulyanova st.  10, Nizhnii Novgorod, 603605, Russia

Keywords: strange attractor, chaotic dynamics, spiral attractor, torus-chaos, homoclinic orbit, invariant curve, three-dimensional Hénon map

Full text: PDF file (4455 kB)
References: PDF file   HTML file
UDC: 517.9
MSC: 37C70, 37C29, 37G25
Received: 06.10.2011
Accepted:24.12.2011

Citation: A. S. Gonchenko, S. V. Gonchenko, L. P. Shilnikov, “Towards scenarios of chaos appearance in three-dimensional maps”, Nelin. Dinam., 8:1 (2012), 3–28

Citation in format AMSBIB
\Bibitem{GonGonShi12}
\by A.~S.~Gonchenko, S.~V.~Gonchenko, L.~P.~Shilnikov
\paper Towards scenarios of chaos appearance in three-dimensional maps
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 1
\pages 3--28
\mathnet{http://mi.mathnet.ru/nd300}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. S. Gonchenko, S. V. Gonchenko, A. O. Kazakov, “O nekotorykh novykh aspektakh khaoticheskoi dinamiki «keltskogo kamnya»”, Nelineinaya dinam., 8:3 (2012), 507–518  mathnet
    2. Borisov A.V., Jalnine A.Yu., Kuznetsov S.P., Sataev I.R., Sedova J.V., “Dynamical Phenomena Occurring Due to Phase Volume Compression in Nonholonomic Model of the Rattleback”, Regul. Chaotic Dyn., 17:6 (2012), 512–532  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. S. P. Kuznetsov, A. Yu. Zhalnin, I. R. Sataev, Yu. V. Sedova, “Fenomeny nelineinoi dinamiki dissipativnykh sistem v negolonomnoi mekhanike «keltskogo kamnya»”, Nelineinaya dinam., 8:4 (2012), 735–762  mathnet
    4. A. P. Kuznetsov, S. P. Kuznetsov, L. V. Tyuryukina, I. R. Sataev, “Stsenarii Landau–Khopfa v ansamble vzaimodeistvuyuschikh ostsillyatorov”, Nelineinaya dinam., 8:5 (2012), 863–873  mathnet
    5. A. S. Gonchenko, S. V. Gonchenko, “O suschestvovanii attraktorov lorentsevskogo tipa v negolonomnoi modeli «keltskogo kamnya»”, Nelineinaya dinam., 9:1 (2013), 77–89  mathnet
    6. A. S. Gonchenko, “Ob attraktorakh lorentsevskogo tipa v modeli keltskogo kamnya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 2, 3–11  mathnet
    7. A. V. Borisov, A. O. Kazakov, S. P. Kuznetsov, “Nonlinear dynamics of the rattleback: a nonholonomic model”, Phys. Usp., 57:5 (2014), 453–460  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    8. A. V. Borisov, A. O. Kazakov, I. R. Sataev, “Regulyarnye i khaoticheskie attraktory v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 10:3 (2014), 361–380  mathnet
    9. A. V. Borisov, A. O. Kazakov, I. R. Sataev, “The reversal and chaotic attractor in the nonholonomic model of Chaplygin's top”, Regul. Chaotic Dyn., 19:6 (2014), 718–733  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    10. Valentin S. Afraimovich, Sergey V. Gonchenko, Lev M. Lerman, Andrey L. Shilnikov, Dmitry V. Turaev, “Scientific Heritage of L.P. Shilnikov”, Regul. Chaotic Dyn., 19:4 (2014), 435–460  mathnet  crossref  mathscinet  zmath
    11. A. Gonchenko, S. Gonchenko, A. Kazakov, D. Turaev,, “Simple scenarios of onset of chaos in three-dimensional maps”, J. Bifur. Chaos Appl. Sci. Engrg., 24:8 (2014), 1440005, 25 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    12. Gonchenko S.V., Ovsyannikov I.I., Tatjer J.C., “Birth of Discrete Lorenz Attractors At the Bifurcations of 3D Maps With Homoclinic Tangencies to Saddle Points”, Regul. Chaotic Dyn., 19:4 (2014), 495–505  crossref  isi
    13. Gonchenko A.S., Gonchenko S.V., “Retracted: Lorenz-Like Attractors in a Nonholonomic Model of a Rattleback (Retracted Article. See Vol. 30, Pg. C3-C3, 2017)”, Nonlinearity, 28:9 (2015), 3403–3417  crossref  isi
    14. I. R. Sataev, A. O. Kazakov, “Stsenarii perekhoda k khaosu v negolonomnoi modeli volchka Chaplygina”, Nelineinaya dinam., 12:2 (2016), 235–250  mathnet  elib
    15. Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Spiral Chaos in the Nonholonomic Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 939–954  mathnet  crossref
    16. A. S. Gonchenko, S. V. Gonchenko, “Variety of strange pseudohyperbolic attractors in three-dimensional generalized Henon maps”, Physica D, 337 (2016), 43–57  crossref  isi
    17. M. Mammeri, “A large chaotic region in a 3-D sinusoid discrete map”, Int. J. Appl. Math. Stat., 55:3 (2016), 133–144  isi
    18. A. S. Gonchenko, A. D. Kozlov, “O stsenariyakh vozniknoveniya khaosa v trekhmernykh neorientiruemykh otobrazheniyakh”, Zhurnal SVMO, 18:4 (2016), 17–29  mathnet  elib
    19. S. Gonchenko, I. Ovsyannikov, “Homoclinic tangencies to resonant saddles and discrete Lorenz attractors”, Discret. Contin. Dyn. Syst.-Ser. S, 10:2 (2017), 273–288  crossref  mathscinet  zmath  isi  scopus
    20. A. D. Kozlov, “Primery strannykh attraktorov v trekhmernykh neorientiruemykh otobrazheniyakh”, Zhurnal SVMO, 19:2 (2017), 62–75  mathnet  crossref  elib
    21. Conchenko A.S., Conchenko V S., Kazakovt V O., Kozlov A.D., “Elements of Contemporary Theory of Dynamical Chaos: a Tutorial. Part i. Pseudohyperbolic Attractors”, Int. J. Bifurcation Chaos, 28:11 (2018), 1830036  crossref  mathscinet  isi  scopus
    22. A. O. Kazakov, A. D. Kozlov, “Nesimmetrichnyi attraktor Lorentsa kak primer novogo psevdogiperbolicheskogo attraktora v trekhmernykh sistemakh”, Zhurnal SVMO, 20:2 (2018), 187–198  mathnet  crossref
    23. Borisov V A., Vetchanin E.V., Mamaev I.S., “Motion of a Smooth Foil in a Fluid Under the Action of External Periodic Forces. i”, Russ. J. Math. Phys., 26:4 (2019), 412–427  crossref  mathscinet  zmath  isi  scopus
    24. Gonchenko A.S., Samylina E.A., “on the Region of Existence of a Discrete Lorenz Attractor in the Nonholonomic Model of a Celtic Stone”, Radiophys. Quantum Electron., 62:5 (2019), 369–384  crossref  isi  scopus
    25. Stankevich N., Kuznetsov A., Popova E., Seleznev E., “Chaos and Hyperchaos Via Secondary Neimark-Sacker Bifurcation in a Model of Radiophysical Generator”, Nonlinear Dyn., 97:4 (2019), 2355–2370  crossref  zmath  isi  scopus
    26. Gonchenko A.S., Gonchenko S.V., Kazakov A.O., Samylina E.A., “Chaotic Dynamics and Multistability in the Nonholonomic Model of a Celtic Stone”, Radiophys. Quantum Electron., 61:10 (2019), 773–786  crossref  isi  scopus
    27. S. V. Gonchenko, A. S. Gonchenko, A. O. Kazakov, A. D. Kozlov, Yu. V. Bakhanova, “Matematicheskaya teoriya dinamicheskogo khaosa i ee prilozheniya: Obzor. Chast 2. Spiralnyi khaos trekhmernykh potokov”, Izvestiya vuzov. PND, 27:5 (2019), 7–52  mathnet  crossref  isi  elib  scopus
    28. Stankevich N., Kazakov A., Gonchenko S., “Scenarios of Hyperchaos Occurrence in 4D Rossler System”, Chaos, 30:12 (2020), 123129  crossref  mathscinet  zmath  isi  scopus
    29. Malykh S., Bakhanova Yu., Kazakov A., Pusuluri K., Shilnikov A., “Homoclinic Chaos in the Rossler Model”, Chaos, 30:11 (2020), 113126  crossref  mathscinet  zmath  isi  scopus
    30. Bakhanova V Yu., Kazakov A.O., Karatetskaia E.Yu., Kozlov A.D., Safonov K.A., “on Homoclinic Attractors of Three-Dimensional Flows”, Izv. Vyss. Uchebn. Zaved.-Prikl. Nelineynaya Din., 28:3 (2020), 231–258  crossref  isi  scopus
    31. E. Kuryzhov, E. Karatetskaia, D. Mints, “Lorenz- and Shilnikov-Shape Attractors in the Model of Two Coupled Parabola Maps”, Rus. J. Nonlin. Dyn., 17:2 (2021), 165–174  mathnet  crossref
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