IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v28y2006i5p1165-1180.html
   My bibliography  Save this article

Study on chaos induced by turbulent maps in noncompact sets

Author

Listed:
  • Shi, Yuming
  • Yu, Pei

Abstract

This paper is concerned with chaos induced by strictly turbulent maps in noncompact sets of complete metric spaces. Two criteria of chaos for such types of maps are established, and then a criterion of chaos, characterized by snap-back repellers in complete metric spaces, is obtained. All the maps presented in this paper are proved to be chaotic either in the sense of both Li–Yorke and Wiggins or in the sense of both Li–Yorke and Devaney. The results weaken the assumptions in some existing criteria of chaos. Several illustrative examples are provided with computer simulation.

Suggested Citation

  • Shi, Yuming & Yu, Pei, 2006. "Study on chaos induced by turbulent maps in noncompact sets," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1165-1180.
  • Handle: RePEc:eee:chsofr:v:28:y:2006:i:5:p:1165-1180
    DOI: 10.1016/j.chaos.2005.08.162
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905008143
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2005.08.162?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Marotto, F.R., 2005. "On redefining a snap-back repeller," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 25-28.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shi, Yuming & Ju, Hyonhui & Chen, Guanrong, 2009. "Coupled-expanding maps and one-sided symbolic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2138-2149.
    2. Kim, Jinhyon & Ju, Hyonhui, 2018. "Hausdorff dimension of the sets of Li-Yorke pairs for some chaotic dynamical systems including A-coupled expanding systems," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 246-251.
    3. Li, Zongcheng & Shi, Yuming & Zhang, Chao, 2008. "Chaos induced by heteroclinic cycles connecting repellers in complete metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 746-761.
    4. Hongyan Zang & Jianying Liu & Jiu Li, 2021. "Construction of a Class of High-Dimensional Discrete Chaotic Systems," Mathematics, MDPI, vol. 9(4), pages 1-20, February.
    5. Kim, Cholsan & Ju, Hyonhui & Chen, Minghao & Raith, Peter, 2015. "A-coupled-expanding and distributional chaos," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 291-295.
    6. Gardini, Laura & Sushko, Iryna & Avrutin, Viktor & Schanz, Michael, 2011. "Critical homoclinic orbits lead to snap-back repellers," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 433-449.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, January.
    2. Jiang, Guirong & Yang, Qigui, 2009. "Complex dynamics in a linear impulsive system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2341-2353.
    3. Liang, Wei & Lv, Xiaolin, 2022. "Li-Yorke chaos in a class of controlled delay difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Ekaterina Ekaterinchuk & Jochen Jungeilges & Tatyana Ryazanova & Iryna Sushko, 2017. "Dynamics of a minimal consumer network with uni-directional influence," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 831-857, November.
    5. Rahman, Aminur & Blackmore, Denis, 2017. "Threshold voltage dynamics of chaotic RS flip-Flops," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 555-566.
    6. Sun, Huijing & Cao, Hongjun, 2007. "Bifurcations and chaos of a delayed ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1383-1393.
    7. Ingrid Kubin & Laura Gardini, 2022. "On the significance of borders: the emergence of endogenous dynamics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 41-62, January.
    8. Gardini, Laura & Hommes, Cars & Tramontana, Fabio & de Vilder, Robin, 2009. "Forward and backward dynamics in implicitly defined overlapping generations models," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 110-129, August.
    9. Stankevich, N.V. & Gonchenko, A.S. & Popova, E.S. & Gonchenko, S.V., 2023. "Complex dynamics of the simplest neuron model: Singular chaotic Shilnikov attractor as specific oscillatory neuron activity," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    10. Zhang, Limin & Wang, Tao, 2023. "Qualitative properties, bifurcations and chaos of a discrete predator–prey system with weak Allee effect on the predator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    11. Dohtani, Akitaka, 2011. "Chaos resulting from nonlinear relations between different variables," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 290-297.
    12. Gardini, Laura & Sushko, Iryna & Avrutin, Viktor & Schanz, Michael, 2011. "Critical homoclinic orbits lead to snap-back repellers," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 433-449.
    13. Chen, Shyan-Shiou & Shih, Chih-Wen, 2009. "Transiently chaotic neural networks with piecewise linear output functions," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 717-730.
    14. Elhafsi Boukhalfa & Elhadj Zeraoulia, 2014. "Existence of Super Chaotic Attractors in a General Piecewise Smooth Map of the Plane," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 12(1), pages 92-98.
    15. A. M. A. El-Sayed & S. M. Salman, 2019. "Dynamical analysis of a complex logistic-type map," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(2), pages 427-450, June.
    16. Salman, S.M. & Yousef, A.M. & Elsadany, A.A., 2016. "Stability, bifurcation analysis and chaos control of a discrete predator-prey system with square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 20-31.
    17. Li, Yan & Wang, Lidong, 2019. "Chaos in a duopoly model of technological innovation with bounded rationality based on constant conjectural variation," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 116-126.
    18. Zhao, Yi & Xie, Lingli & Yiu, K.F. Cedric, 2009. "An improvement on Marotto’s theorem and its applications to chaotification of switching systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2225-2232.
    19. Deng, Liuchun & Khan, M. Ali, 2018. "On Mitra’s sufficient condition for topological chaos: Seventeen years later," Economics Letters, Elsevier, vol. 164(C), pages 70-74.
    20. Gao, Yinghui, 2009. "Complex dynamics in a two-dimensional noninvertible map," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1798-1810.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:28:y:2006:i:5:p:1165-1180. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.