IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v161y2022ics0960077922005975.html
   My bibliography  Save this article

Bifurcation and chaos in one dimensional chains of small particles

Author

Listed:
  • Simas, Fabiano C.
  • Nobrega, K.Z.
  • Bazeia, D.

Abstract

This work deals with bifurcation and the chaotic behavior in one dimensional chains of small particles. We consider two distinct possibilities, one where the particles are modeled by a fourth-order potential which was already studied. We revisit this system and bring novelties concerning the presence of the three-armed star behavior and the study of the corresponding Lyapunov exponent. The other system is new, and there the particles are more involved and modeled by an eighth-order potential. We investigate this new system within the same approach, emphasizing the behavior of the orbits, the bifurcation profile and the corresponding Lyapunov exponent.

Suggested Citation

  • Simas, Fabiano C. & Nobrega, K.Z. & Bazeia, D., 2022. "Bifurcation and chaos in one dimensional chains of small particles," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005975
    DOI: 10.1016/j.chaos.2022.112387
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922005975
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112387?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. Michael Hoffmann & Franz P. G. Fengler & Melanie Herzig & Terence Mittmann & Benjamin Max & Uwe Schroeder & Raluca Negrea & Pintilie Lucian & Stefan Slesazeck & Thomas Mikolajick, 2019. "Unveiling the double-well energy landscape in a ferroelectric layer," Nature, Nature, vol. 565(7740), pages 464-467, January.
    2. Jing, Zhujun & Yang, Jianping, 2006. "Bifurcation and chaos in discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 259-277.
    3. Huang, Tousheng & Zhang, Huayong, 2016. "Bifurcation, chaos and pattern formation in a space- and time-discrete predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 92-107.
    Full references (including those not matched with items on IDEAS)

    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. Zhong, Shihong & Xia, Juandi & Liu, Biao, 2021. "Spatiotemporal dynamics analysis of a semi-discrete reaction-diffusion Mussel-Algae system with advection," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Wang, Jinliang & Li, You & Zhong, Shihong & Hou, Xiaojie, 2019. "Analysis of bifurcation, chaos and pattern formation in a discrete time and space Gierer Meinhardt system," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 1-17.
    3. Xu, Li & Liu, Jiayi & Zhang, Guang, 2018. "Pattern formation and parameter inversion for a discrete Lotka–Volterra cooperative system," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 226-231.
    4. Wang, Jiang & Chen, Liangquan & Fei, Xianyang, 2007. "Bifurcation control of the Hodgkin–Huxley equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 217-224.
    5. Chen, Yanguang, 2009. "Spatial interaction creates period-doubling bifurcation and chaos of urbanization," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1316-1325.
    6. Tousheng Huang & Huayong Zhang & Xuebing Cong & Ge Pan & Xiumin Zhang & Zhao Liu, 2019. "Exploring Spatiotemporal Complexity of a Predator-Prey System with Migration and Diffusion by a Three-Chain Coupled Map Lattice," Complexity, Hindawi, vol. 2019, pages 1-19, May.
    7. Sun, Huijing & Cao, Hongjun, 2007. "Bifurcations and chaos of a delayed ecological model," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1383-1393.
    8. Wang, Jiang & Chen, Liangquan & Fei, Xianyang, 2007. "Analysis and control of the bifurcation of Hodgkin–Huxley model," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 247-256.
    9. Xu, Rui & Ma, Zhien, 2008. "Stability and Hopf bifurcation in a ratio-dependent predator–prey system with stage structure," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 669-684.
    10. Abernethy, Gavin M. & McCartney, Mark & Glass, David H., 2019. "The role of migration in a spatial extension of the Webworld eco-evolutionary model," Ecological Modelling, Elsevier, vol. 397(C), pages 122-140.
    11. Lv, Jian Cheng & Yi, Zhang, 2007. "Stability and chaos of LMSER PCA learning algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1440-1447.
    12. Zhenyu Sun & Yueqi Su & Aomiao Zhi & Zhicheng Gao & Xu Han & Kang Wu & Lihong Bao & Yuan Huang & Youguo Shi & Xuedong Bai & Peng Cheng & Lan Chen & Kehui Wu & Xuezeng Tian & Changzheng Wu & Baojie Fen, 2024. "Evidence for multiferroicity in single-layer CuCrSe2," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    13. Yulong Huang & Jennifer L. Gottfried & Arpita Sarkar & Gengyi Zhang & Haiqing Lin & Shenqiang Ren, 2023. "Proton-controlled molecular ionic ferroelectrics," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    14. Yijie Li & Zhiming Guo, 2022. "Wolbachia Invasion Dynamics by Integrodifference Equations," Mathematics, MDPI, vol. 10(22), pages 1-13, November.
    15. Matvey Kulakov & Efim Frisman, 2023. "Clustering Synchronization in a Model of the 2D Spatio-Temporal Dynamics of an Age-Structured Population with Long-Range Interactions," Mathematics, MDPI, vol. 11(9), pages 1-21, April.
    16. 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).
    17. Michael Hoffmann & Zheng Wang & Nujhat Tasneem & Ahmad Zubair & Prasanna Venkatesan Ravindran & Mengkun Tian & Anthony Arthur Gaskell & Dina Triyoso & Steven Consiglio & Kandabara Tapily & Robert Clar, 2022. "Antiferroelectric negative capacitance from a structural phase transition in zirconia," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    18. Jialin Chen & Xiaqing He & Fengde Chen, 2021. "The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource," Mathematics, MDPI, vol. 9(8), pages 1-20, April.
    19. Zhang, Xue & Zhang, Qing-ling & Zhang, Yue, 2009. "Bifurcations of a class of singular biological economic models," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1309-1318.
    20. Lv, Jian Cheng & Yi, Zhang, 2007. "Some chaotic behaviors in a MCA learning algorithm with a constant learning rate," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1040-1047.

    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:161:y:2022:i:c:s0960077922005975. 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.