Can a border collision bifurcation of a chaotic attractor lead to its expansion?

被引:0
作者
Avrutin, Viktor [1 ]
Panchuk, Anastasiia [2 ]
Sushko, Iryna [2 ]
机构
[1] Univ Stuttgart, Inst Syst Theory & Automat Control, Stuttgart, Germany
[2] Natl Acad Sci Ukraine, Inst Math, Kiev, Ukraine
来源
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2023年 / 479卷 / 2277期
关键词
piecewise smooth systems; one-dimensional maps; chaotic attractors; border collision bifurcations; CRITICAL EXPONENTS; ORBITS; CRISIS; MAPS;
D O I
10.1098/rspa.2023.0260
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Recently, we reported that a chaotic attractor in a discontinuous one-dimensional map may undergo a so-called exterior border collision bifurcation, which causes additional bands of the attractor to appear. In the present paper, we suppose that the chaotic attractor's basin boundary contains a chaotic repeller, and discuss a bifurcation pattern consisting of an exterior border collision bifurcation and an expansion bifurcation (interior crisis). In the generic case, where neither the border point the chaotic attractor collides with, nor any of its images belong to the chaotic repeller, the exterior border collision bifurcation is followed by the expansion bifurcation, and the distance between both bifurcations may be arbitrarily small but positive. In the non-generic (codimension-2) case, these bifurcations occur simultaneously, so that a border collision bifurcation of a chaotic attractor leads directly to its expansion.
引用
收藏
页数:23
相关论文
共 32 条
  • [1] [Anonymous], 2009, Nonlinear oligopolies: stability and bifurcations
  • [2] Avrutin V., 2019, CONTINUOUS DISCONTIN
  • [3] Border collision bifurcations of chaotic attractors in one-dimensional maps with multiple discontinuities
    Avrutin, Viktor
    Panchuk, Anastasiia
    Sushko, Iryna
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2021, 477 (2253):
  • [4] Bifurcations of hidden orbits in discontinuous maps
    Avrutin, Viktor
    Jeffrey, Mike R.
    [J]. NONLINEARITY, 2021, 34 (09) : 6140 - 6172
  • [5] Bifurcations of Chaotic Attractors in One-Dimensional Piecewise Smooth Maps
    Avrutin, Viktor
    Gardini, Laura
    Schanz, Michael
    Sushko, Iryna
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (08):
  • [6] Robust chaos
    Banerjee, S
    Yorke, JA
    Grebogi, C
    [J]. PHYSICAL REVIEW LETTERS, 1998, 80 (14) : 3049 - 3052
  • [7] Banerjee S., 2001, NONLINEAR PHENOMENA
  • [8] Brogliato B., 1999, Nonsmooth Mechanics
  • [9] DiBernardo M, 2008, APPL MATH SCI, V163, P1, DOI 10.1007/978-1-84628-708-4
  • [10] Fournier-Prunaret D., 1997, Grazer Math. Berichte, V334, P77