IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip1s0960077921008638.html
   My bibliography  Save this article

Spatiotemporal complexity in a Leslie-Gower type predator-prey model near Turing-Hopf point

Author

Listed:
  • Chen, Mengxin
  • Wu, Ranchao
  • Liu, Hongxia
  • Fu, Xiaoxue

Abstract

The Leslie-Gower type predator-prey system with the ratio-dependent Holling III functional response and Neumann boundary conditions is investigated in this paper. First, the boundedness results of both parabolic and elliptic equations are presented. Hereafter, the existence of the codimension-two Turing-Hopf point (C2THP) is identified, where the Turing and the Hopf modes intersect. To further explore the spatiotemporal dynamics near the C2THP, it is necessary to derive the amplitude equations, however, there are few results about that in the two-dimensional domain. Here the method of weakly nonlinear analysis is adopted to derive the amplitude equations. The temporal patterns, hexagonal patterns, and plane wave patterns, as well as the sufficient conditions of their existence and stability, can be presented through amplitude equations.

Suggested Citation

  • Chen, Mengxin & Wu, Ranchao & Liu, Hongxia & Fu, Xiaoxue, 2021. "Spatiotemporal complexity in a Leslie-Gower type predator-prey model near Turing-Hopf point," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921008638
    DOI: 10.1016/j.chaos.2021.111509
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921008638
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111509?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. Shi, Hong-Bo & Li, Yan, 2015. "Global asymptotic stability of a diffusive predator–prey model with ratio-dependent functional response," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 71-77.
    2. Zheng, Qianqian & Shen, Jianwei, 2020. "Turing instability induced by random network in FitzHugh-Nagumo model," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    3. Chen, Mengxin & Wu, Ranchao & Chen, Liping, 2020. "Spatiotemporal patterns induced by Turing and Turing-Hopf bifurcations in a predator-prey system," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    4. Ghorai, Santu & Poria, Swarup, 2016. "Turing patterns induced by cross-diffusion in a predator-prey system in presence of habitat complexity," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 421-429.
    5. Xue, Qiang & Liu, Chen & Li, Li & Sun, Gui-Quan & Wang, Zhen, 2021. "Interactions of diffusion and nonlocal delay give rise to vegetation patterns in semi-arid environments," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    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. Chen, Mengxin & Zheng, Qianqian, 2022. "Predator-taxis creates spatial pattern of a predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Chen, Mengxin & Zheng, Qianqian, 2023. "Diffusion-driven instability of a predator–prey model with interval biological coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    3. Chen, Mengxin & Ham, Seokjun & Choi, Yongho & Kim, Hyundong & Kim, Junseok, 2023. "Pattern dynamics of a harvested predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 176(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. Souna, Fethi & Belabbas, Mustapha & Menacer, Youssaf, 2023. "Complex pattern formations induced by the presence of cross-diffusion in a generalized predator–prey model incorporating the Holling type functional response and generalization of habitat complexity e," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 597-618.
    2. Shivam, & Singh, Kuldeep & Kumar, Mukesh & Dubey, Ramu & Singh, Teekam, 2022. "Untangling role of cooperative hunting among predators and herd behavior in prey with a dynamical systems approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Chen, Mengxin & Ham, Seokjun & Choi, Yongho & Kim, Hyundong & Kim, Junseok, 2023. "Pattern dynamics of a harvested predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    4. Ma, Yuanyuan & Dong, Nan & Liu, Na & Xie, Leilei, 2022. "Spatiotemporal and bifurcation characteristics of a nonlinear prey-predator model," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    5. Li, Qiang & Liu, Zhijun & Yuan, Sanling, 2019. "Cross-diffusion induced Turing instability for a competition model with saturation effect," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 64-77.
    6. Ghorai, Santu & Bairagi, Nandadulal, 2022. "Instabilities in hyperbolic reaction–diffusion system with cross diffusion and species-dependent inertia," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    7. Arancibia-Ibarra, Claudio & Aguirre, Pablo & Flores, José & van Heijster, Peter, 2021. "Bifurcation analysis of a predator-prey model with predator intraspecific interactions and ratio-dependent functional response," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    8. Zhao, Xin & Zeng, Zhijun, 2020. "Stationary distribution and extinction of a stochastic ratio-dependent predator–prey system with stage structure for the predator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    9. Hu, Junlang & Zhu, Linhe, 2021. "Turing pattern analysis of a reaction-diffusion rumor propagation system with time delay in both network and non-network environments," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    10. Liu, Chen & Wang, Fang-Guang & Xue, Qiang & Li, Li & Wang, Zhen, 2022. "Pattern formation of a spatial vegetation system with root hydrotropism," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    11. Yangyang Shao & Yan Meng & Xinyue Xu, 2022. "Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    12. Wang, Caiyun, 2015. "Rich dynamics of a predator–prey model with spatial motion," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 1-9.
    13. Chen, Mengxin & Wu, Ranchao, 2023. "Steady states and spatiotemporal evolution of a diffusive predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    14. Bhunia, Bidhan & Ghorai, Santu & Kar, Tapan Kumar & Biswas, Samir & Bhutia, Lakpa Thendup & Debnath, Papiya, 2023. "A study of a spatiotemporal delayed predator–prey model with prey harvesting: Constant and periodic diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    15. Lv, Yehu, 2022. "The spatially homogeneous hopf bifurcation induced jointly by memory and general delays in a diffusive system," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    16. Zhu, Linhe & Tang, Yuxuan & Shen, Shuling, 2023. "Pattern study and parameter identification of a reaction-diffusion rumor propagation system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    17. Zheng, Qianqian & Shen, Jianwei & Pandey, Vikas & Guan, Linan & Guo, Yantao, 2023. "Turing instability in a network-organized epidemic model with delay," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    18. Zheng, Qianqian & Shen, Jianwei & Xu, Yong & Pandey, Vikas & Guan, Linan, 2022. "Pattern mechanism in stochastic SIR networks with ER connectivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    19. Chen, Zheng & Liu, Jieyu & Li, Li & Wu, Yongping & Feng, Guolin & Qian, Zhonghua & Sun, Gui-Quan, 2022. "Effects of climate change on vegetation patterns in Hulun Buir Grassland," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    20. Yang, Ruizhi & Ma, Jian, 2018. "Analysis of a diffusive predator-prey system with anti-predator behaviour and maturation delay," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 128-139.

    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:153:y:2021:i:p1:s0960077921008638. 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.