Periods 1 + 2 imply chaos in steep or nonsmooth maps

Autor: Mike R Jeffrey, Viktor Avrutin

Publikováno v: Jeffrey, M R & Avrutin, V 2022, ' Periods 1+2 implies chaos in steep or nonsmooth maps ', Nonlinearity, vol. 35, no. 12 . https://doi.org/10.1088/1361-6544/ac9506

Maps with discontinuities can be shown to have many of the same properties of continuous maps if we include hidden orbits—solutions that include points lying on a discontinuity. We show here how the well known property that ‘period 3 implies chao

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::61e01cf15d0252a392c14ecea3377d41
https://doi.org/10.1088/1361-6544/ac9506

Bifurcation Structures in a Bimodal Piecewise Linear Map

Autor: Anastasiia Panchuk, Iryna Sushko, Viktor Avrutin

Publikováno v: Frontiers in Applied Mathematics and Statistics, Vol 3 (2017)

In this paper we present an overview of the results concerning dynamics of a piecewise linear bimodal map. The organizing principles of the bifurcation structures in both regular and chaotic domains of the parameter space of the map are discussed. In

Externí odkaz: https://doaj.org/article/6ec99af3bc834ed99749ba7050bcf74a

Non-visible transformations of chaotic attractors due to their ultra-low density in AC–DC power factor correction converters

Autor: Viktor Avrutin, Abdelali El Aroudi, Zhanybai T. Zhusubaliyev

Publikováno v: Nonlinear Dynamics. 102:2905-2924

Recently, it has been shown that DC–AC and AC–DC power converters whose dynamics is governed by two vastly different frequencies lead to a special class of piecewise smooth models characterized by a practically unpredictable number of switching m

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::6467e96b6a6cb369d3e5b3a3c754b2e6
https://doi.org/10.1007/s11071-020-06077-5

Center Bifurcation in the Lozi Map

Autor: Iryna Sushko, Viktor Avrutin, Laura Gardini

Publikováno v: International Journal of Bifurcation and Chaos. 31

We consider the well-known Lozi map, which is a 2D piecewise linear map depending on two parameters. This map can be considered as a piecewise linear analog of the Hénon map, allowing to simplify the rigorous proof of the existence of a chaotic attr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c69fc6a4606790ed418a5b1231062081
https://doi.org/10.1142/s0218127421300469

Non-observable chaos in piecewise smooth systems

Autor: Zhanybai T. Zhusubaliyev, Viktor Avrutin, Abdelali El Aroudi, Dan Suissa

Publikováno v: Nonlinear Dynamics. 99:2031-2048

In the present paper, we discuss bifurcations of chaotic attractors in piecewise smooth one-dimensional maps with a high number of switching manifolds. As an example, we consider models of DC/AC power electronic converters (inverters). We demonstrate

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::fffc4eaecffb45c01941f3b256dacf87
https://doi.org/10.1007/s11071-019-05406-7