IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v166y2023ics096007792201089x.html
   My bibliography  Save this article

Bifurcation and turing instability analysis for a space- and time-discrete predator–prey system with Smith growth function

Author

Listed:
  • Han, Xiaoling
  • Lei, Ceyu

Abstract

In this paper, the dynamic behavior of a space- and time-discrete predator–prey system with Smith growth function is studied. Through the stability analysis, the parametric conditions are gained to ensure the stability of the homogeneous steady state of the system. Through the bifurcation theory, the expressions of the critical values for the occurrence of Neimark–Sacker bifurcation and flip bifurcation of the system are obtained, and the conditions for the occurrence of Turing bifurcation of the system are given. Finally, through numerical simulation, we can observe some complex dynamic behaviors, such as period-doubling cascade, invariant circles, periodic windows, chaotic dynamics and pattern formation.

Suggested Citation

  • Han, Xiaoling & Lei, Ceyu, 2023. "Bifurcation and turing instability analysis for a space- and time-discrete predator–prey system with Smith growth function," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s096007792201089x
    DOI: 10.1016/j.chaos.2022.112910
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792201089X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.112910?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. A. Q. Khan & E. Abdullah & Tarek F. Ibrahim, 2020. "Supercritical Neimark–Sacker Bifurcation and Hybrid Control in a Discrete-Time Glycolytic Oscillator Model," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-15, January.
    2. Li, Meifeng & Han, Bo & Xu, Li & Zhang, Guang, 2013. "Spiral patterns near Turing instability in a discrete reaction diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 49(C), pages 1-6.
    3. 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.
    4. 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)

    Citations

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


    Cited by:

    1. Li, Tianhua & Zhang, Xuetian & Zhang, Chunrui, 2024. "Pattern dynamics analysis of a space–time discrete spruce budworm model," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).

    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. 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.
    2. 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).
    3. 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.
    4. Lu, Guangqing & Smidtaite, Rasa & Howard, Daniel & Ragulskis, Minvydas, 2019. "An image hiding scheme in a 2-dimensional coupled map lattice of matrices," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 78-85.
    5. Zhang, Guang & Zhang, Ruixuan & Yan, Yubin, 2020. "The diffusion-driven instability and complexity for a single-handed discrete Fisher equation," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    6. Li, Tianhua & Zhang, Xuetian & Zhang, Chunrui, 2024. "Pattern dynamics analysis of a space–time discrete spruce budworm model," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    7. He, Haoming & Xiao, Min & He, Jiajin & Zheng, Weixing, 2024. "Regulating spatiotemporal dynamics for a delay Gierer–Meinhardt model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    8. 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.
    9. 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.
    10. Ghosh, Joydev & Sahoo, Banshidhar & Poria, Swarup, 2017. "Prey-predator dynamics with prey refuge providing additional food to predator," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 110-119.
    11. 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).
    12. 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.
    13. 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.
    14. Flores, J.C., 2020. "Game theory approach to sterile release populations and replicator dynamics: Niche fragmentation and resilience," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    15. Kaya, Guven & Kartal, Senol & Gurcan, Fuat, 2020. "Dynamical analysis of a discrete conformable fractional order bacteria population model in a microcosm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    16. 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).
    17. Zhang, Huayong & Ma, Shengnan & Huang, Tousheng & Cong, Xuebing & Yang, Hongju & Zhang, Feifan, 2018. "A new finding on pattern self-organization along the route to chaos," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 118-130.
    18. 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.
    19. Zhang, Yin & Wu, Fuqiang & Wang, Chunni & Ma, Jun, 2019. "Stability of target waves in excitable media under electromagnetic induction and radiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 519-530.

    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:166:y:2023:i:c:s096007792201089x. 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.