IDEAS home Printed from https://ideas.repec.org/a/wly/complx/v2022y2022i1n2823303.html

Spatiotemporal Evolution Characteristics of Time‐Delay Ecological Competition Systems with Food‐Limited and Diffusion

Author

Listed:
  • Feilong Wang
  • Min Xiao
  • Zhengxin Wang
  • Jing Zhao
  • Gong Chen
  • Jinde Cao

Abstract

In this paper, we put forward a time‐delay ecological competition system with food restriction and diffusion terms under Neumann boundary conditions. For the case without delay, the conditions for local asymptotic stability and Turing instability are constructed. For the case with delay, the existence of Hopf bifurcation is demonstrated by analyzing the root distribution of the corresponding characteristic equations. Furthermore, by using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulas are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, some simulation examples are provided to substantiate our analysis.

Suggested Citation

  • Feilong Wang & Min Xiao & Zhengxin Wang & Jing Zhao & Gong Chen & Jinde Cao, 2022. "Spatiotemporal Evolution Characteristics of Time‐Delay Ecological Competition Systems with Food‐Limited and Diffusion," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:2823303
    DOI: 10.1155/2022/2823303
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2022/2823303
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2022/2823303?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
    ---><---

    References listed on IDEAS

    as
    1. Hua Liu & Yong Ye & Yumei Wei & Weiyuan Ma & Ming Ma & Kai Zhang, 2019. "Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay," Complexity, Hindawi, vol. 2019, pages 1-14, November.
    2. Mortuja, Md Golam & Chaube, Mithilesh Kumar & Kumar, Santosh, 2021. "Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    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. Ye Xuan Li & Hua Liu & Yu Mei Wei & Ming Ma & Gang Ma & Jing Yan Ma, 2022. "Population Dynamic Study of Prey‐Predator Interactions with Weak Allee Effect, Fear Effect, and Delay," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    2. Zhou, Jiaying & Ye, Yong & Arenas, Alex & Gómez, Sergio & Zhao, Yi, 2023. "Pattern formation and bifurcation analysis of delay induced fractional-order epidemic spreading on networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Yao, Yong, 2025. "Dynamics of a Leslie–Gower type predator–prey system with herd behavior and constant harvesting in prey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 32-49.
    4. Sarif, Nawaj & Kumar, Arjun & Anshu, & Sarwardi, Sahabuddin & Dubey, Balram, 2024. "Spatio-temporal dynamics in a delayed prey–predator model with nonlinear prey refuge and harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    5. Sozan Fuad Aziz & Hanaa Jamal Ahmed & Saiwan Majeed Fatah & Arkan Nawzad Mustafa, 2025. "Local Bifurcation and Global Stability of an Eco‐Epidemiological Model Incorporating Fear Effect and Prey Harvesting," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    6. Li, Zhenlei & Zhang, Yue, 2024. "Dynamic analysis of a fast slow modified Leslie–Gower predator–prey model with constant harvest and stochastic factor," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 474-499.
    7. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    8. Huangyu Guo & Jing Han & Guodong Zhang, 2023. "Hopf Bifurcation and Control for the Bioeconomic Predator–Prey Model with Square Root Functional Response and Nonlinear Prey Harvesting," Mathematics, MDPI, vol. 11(24), pages 1-18, December.
    9. Anita Triska & Agus Yodi Gunawan & Nuning Nuraini, 2023. "The Effects of the Susceptible and Infected Cross-Diffusion Terms on Pattern Formations in an SI Model," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
    10. 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).
    11. Haiyin Li & Xuhua Cheng, 2021. "Dynamics of Stage-Structured Predator–Prey Model with Beddington–DeAngelis Functional Response and Harvesting," Mathematics, MDPI, vol. 9(17), pages 1-15, September.
    12. Lei Shi & Jiaying Zhou & Yong Ye, 2023. "Pattern Formation in a Predator–Prey Model with Allee Effect and Hyperbolic Mortality on Multiplex Networks," Mathematics, MDPI, vol. 11(15), pages 1-15, July.

    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:wly:complx:v:2022:y:2022:i:1:n:2823303. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/8503 .

    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.