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This article is cited in 6 scientific papers (total in 6 papers)
Universal two-dimensional map and its radiophysical realization
Alexander P. Kuznetsova, Sergey P. Kuznetsova, Mikhail V. Pozdnyakovb, Julia V. Sedovaa a Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch Zelenaya 38, Saratov, 410019 Russia
b Saratov State Technical University Polytechnicheskaya 77, Saratov, 410054, Russia
Abstract:
We suggest a simple two-dimensional map, parameters of which are the trace and Jacobian of the perturbation matrix of the fixed point. On the parameters plane it demonstrates the main universal bifurcation scenarios: the threshold to chaos via period-doublings, the situation of quasiperiodic oscillations and Arnold tongues. We demonstrate the possibility of implementation of such map in radiophysical device.
Keywords:
maps, bifurcations, phenomena of quasiperiodicity
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UDC:
517.9
MSC: 37G35 Received: 27.02.2012 Revised: 16.04.2012
Citation:
Alexander P. Kuznetsov, Sergey P. Kuznetsov, Mikhail V. Pozdnyakov, Julia V. Sedova, “Universal two-dimensional map and its radiophysical realization”, Nelin. Dinam., 8:3 (2012), 461–471
Citation in format AMSBIB
\Bibitem{KuzKuzPoz12}
\by Alexander~P.~Kuznetsov, Sergey~P.~Kuznetsov, Mikhail~V.~Pozdnyakov, Julia~V.~Sedova
\paper Universal two-dimensional map and its radiophysical realization
\jour Nelin. Dinam.
\yr 2012
\vol 8
\issue 3
\pages 461--471
\mathnet{http://mi.mathnet.ru/nd335}
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http://mi.mathnet.ru/eng/nd335 http://mi.mathnet.ru/eng/nd/v8/i3/p461
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A. P. Kuznetsov, M. V. Pozdnyakov, Yu. V. Sedova, “Svyazannye universalnye otobrazheniya s bifurkatsiei Neimarka–Sakera”, Nelineinaya dinam., 8:3 (2012), 473–482
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G. P. Neverova, E. Ya. Frisman, “Matematicheskoe modelirovanie dinamiki lokalnykh odnorodnykh populyatsii s uchetom effektov zapazdyvaniya”, Matem. biologiya i bioinform., 10:2 (2015), 309–324
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O. L. Revutskaya, G. P. Neverova, M. P. Kulakov, E. Ya. Frisman, “Model dinamiki chislennosti dvukhvozrastnoi populyatsii: ustoichivost, multistabilnost i khaos”, Nelineinaya dinam., 12:4 (2016), 591–603
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Neverova G.P., Zhdanova O.L., Ghosh B., Frisman E.Ya., “Dynamics of a Discrete-Time Stage-Structured Predator-Prey System With Holling Type II Response Function”, Nonlinear Dyn., 98:1 (2019), 427–446
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S. D. Glyzin, S. A. Kaschenko, “Semeistvo konechnomernykh otobrazhenii, indutsirovannykh logisticheskim uravneniem s zapazdyvaniem”, Matem. modelirovanie, 32:3 (2020), 19–46
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G. P. Neverova, E. Ya. Frisman, “Rezhimy dinamiki populyatsii s neperekryvayuschimisya pokoleniyami s uchetom geneticheskoi i stadiinoi struktur”, Kompyuternye issledovaniya i modelirovanie, 12:5 (2020), 1165–1190
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