Abstract:
Ensembles of several Rössler chaotic oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of different and sufficiently high dimensional invariant tori. The possibility of a quasi-periodic Hopf bifurcation and a cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonance tori are revealed. Boundaries of these domains correspond to the saddle-node bifurcations. Inside the domains of resonance modes, torus-doubling bifurcations and destruction of tori are observed.
This work was supported by the Russian Foundation for Basic Research grant No.14-02-00085 and by RF Presidential program for leading Russian research schools NSh-1726.2014.
Citation:
Alexander P. Kuznetsov, Natalia A. Migunova, Igor R. Sataev, Yuliya V. Sedova, Ludmila V. Turukina, “From Chaos to Quasi-Periodicity”, Regul. Chaotic Dyn., 20:2 (2015), 189–204
\Bibitem{KuzMigSat15}
\by Alexander P. Kuznetsov, Natalia A. Migunova, Igor R. Sataev, Yuliya V. Sedova, Ludmila V. Turukina
\paper From Chaos to Quasi-Periodicity
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 2
\pages 189--204
\mathnet{http://mi.mathnet.ru/rcd53}
\crossref{https://doi.org/10.1134/S1560354715020070}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3332951}
\zmath{https://zbmath.org/?q=an:06468713}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2015RCD....20..189K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000352483000007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84928261491}
Linking options:
https://www.mathnet.ru/eng/rcd53
https://www.mathnet.ru/eng/rcd/v20/i2/p189
This publication is cited in the following 19 articles:
A.P. Kuznetsov, L.V. Turukina, “About the chaos influence on a system with multi-frequency quasi-periodicity and the Landau-Hopf scenario”, Physica D: Nonlinear Phenomena, 2024, 134425
Nickolai Shadrin, Natalia Mirzoeva, Vladislav Proskurnin, Elena Anufriieva, “The vertical distribution of 27 elements in bottom sediments reflects the modern history of the hypersaline lagoon”, Regional Studies in Marine Science, 67 (2023), 103183
Alexander P. Kuznetsov, Yuliya V. Sedova, Nataliya V. Stankevich, “Coupled systems with quasi-periodic and chaotic dynamics”, Chaos, Solitons & Fractals, 169 (2023), 113278
Alexander P. Kuznetsov, Yuliya V. Sedova, Nataliya V. Stankevich, “Discrete Rössler Oscillators: Maps and Their Ensembles”, Int. J. Bifurcation Chaos, 33:15 (2023)
Alberto T. Pérez, “Numerical analysis on transition sequence and heat transfer capacity of film boiling with a uniform electric field”, Physics of Fluids, 35:5 (2023)
Qi Wang, Yifei Guan, Tao Wei, Jian Wu, “Transition sequences and heat transfer enhancement in electro-thermo-convection of a dielectric liquid between two parallel electrodes”, International Journal of Thermal Sciences, 179 (2022), 107705
Wang Q., Guan Y., Huang J., Wu J., “Chaotic Electro-Convection Flow States of a Dielectric Liquid Between Two Parallel Electrodes”, Eur. J. Mech. B-Fluids, 89 (2021), 332–348
Dudkowski D., Wojewoda J., Czolczynski K., Kapitaniak T., “Experimental Chaotic Synchronization For Coupled Double Pendula”, Chaos, 31:6 (2021), 061107
Kuznetsov A.P., Stankevich V N., Shchegoleva N.A., “Synchronization of Coupled Generators of Quasi-Periodic Oscillations Upon Destruction of Invariant Curve”, Izv. Vyss. Uchebn. Zaved.-Prikl. Nelineynaya Din., 29:1 (2021), 136–159
F. Li, Ch. Tai, H. Bao, J. Luo, B. Bao, “Hyperchaos, quasi-period and coexisting behaviors in second-order-memristor-based jerk circuit”, Eur. Phys. J.-Spec. Top., 229:6-7 (2020), 1045–1058
Y. Lin, W. B. Liu, H. Bao, Q. Shen, “Bifurcation mechanism of periodic bursting in a simple three-element-based memristive circuit with fast-slow effect”, Chaos Solitons Fractals, 131 (2020), 109524
A. P. Kuznetsov, S. P. Kuznetsov, N. A. Shchegoleva, N. V. Stankevich, “Dynamics of coupled generators of quasiperiodic oscillations: different types of synchronization and other phenomena”, Physica D, 398 (2019), 1–12
N. Stankevich, A. Kuznetsov, E. Popova, E. Seleznev, “Chaos and hyperchaos via secondary Neimark–Sacker bifurcation in a model of radiophysical generator”, Nonlinear Dyn., 97:4 (2019), 2355–2370
B. C. Bao, P. Y. Wu, H. Bao, Q. Xu, M. Chen, “Numerical and experimental confirmations of quasi-periodic behavior and chaotic bursting in third-order autonomous memristive oscillator”, Chaos Solitons Fractals, 106 (2018), 161–170
S. P. Kuznetsov, V. P. Kruglov, “On some simple examples of mechanical systems with hyperbolic chaos”, Proc. Steklov Inst. Math., 297 (2017), 208–234
S. Das, Y. Saiki, E. Sander, J. A. Yorke, “Quantitative quasiperiodicity”, Nonlinearity, 30:11 (2017), 4111–4140
S. Das, Ch. B. Dock, Y. Saiki, M. Salgado-Flores, E. Sander, J. Wu, J. A. Yorke, “Measuring quasiperiodicity”, EPL, 114:4 (2016), 40005
Sergey P. Kuznetsov, “Plate Falling in a Fluid: Regular and Chaotic Dynamics of Finite-dimensional Models”, Regul. Chaotic Dyn., 20:3 (2015), 345–382
Citation in format AMSBIB
Contact us: