IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v150y2021ics0960077921004550.html
   My bibliography  Save this article

Study of periodic diffusion and time delay induced spatiotemporal patterns in a predator-prey system

Author

Listed:
  • Tao, Xiangyu
  • Zhu, Linhe

Abstract

In this paper, we establish a diffusion-reaction predator-prey model with Allee effect and time delay. For this model, we mainly study the effects of time delay and periodic diffusion on the stability of the equilibrium point and the formation of Turing pattern. First, we theoretically analyze the conditions of Turing instability caused by the time delay and periodic diffusion. At the same time, through a large number of numerical simulations, we verify the existence of spatiotemporal patterns and obtain that the pattern in the formation process not only appears the spots, strips, but also exists the coexistence of spots and strips. In addition, it also appears the labyrinth pattern under some suitable parameters. The final comparisons show that periodic diffusion, time delay and Allee effect all play an important role in the formation of Turing pattern.

Suggested Citation

  • Tao, Xiangyu & Zhu, Linhe, 2021. "Study of periodic diffusion and time delay induced spatiotemporal patterns in a predator-prey system," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004550
    DOI: 10.1016/j.chaos.2021.111101
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921004550
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111101?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. Lu, Yang & Li, Dan & Liu, Shengqiang, 2016. "Modeling of hunting strategies of the predators in susceptible and infected prey," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 268-285.
    2. Miao Peng & Zhengdi Zhang & C. W. Lim & Xuedi Wang, 2018. "Hopf Bifurcation and Hybrid Control of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate and Holling Type II Functional Response," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-12, June.
    3. Xia, Chengyi & Wang, Juan & Wang, Li & Sun, Shiwen & Sun, Junqing & Wang, Jinsong, 2012. "Role of update dynamics in the collective cooperation on the spatial snowdrift games: Beyond unconditional imitation and replicator dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1239-1245.
    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. Li, Xiaopeng & Sun, Shiwen & Xia, Chengyi, 2019. "Reputation-based adaptive adjustment of link weight among individuals promotes the cooperation in spatial social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 810-820.
    6. Bao, Xiaomei & Tian, Canrong, 2019. "Delay driven vegetation patterns of a plankton system on a network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 74-88.
    7. Zhu, Linhe & Liu, Wenshan & Zhang, Zhengdi, 2020. "Delay differential equations modeling of rumor propagation in both homogeneous and heterogeneous networks with a forced silence function," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    8. Wenping Xue & Kangji Li & Guohai Liu, 2016. "DDI-based finite-time stability analysis for nonlinear switched systems with time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(12), pages 3027-3035, September.
    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. Qi Quan & Xiangjun Dai & Jianjun Jiao, 2023. "Dynamics of a Predator–Prey Model with Impulsive Diffusion and Transient/Nontransient Impulsive Harvesting," Mathematics, MDPI, vol. 11(14), pages 1-25, July.
    2. 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).
    3. Bi, Zhimin & Liu, Shutang & Ouyang, Miao, 2022. "Spatial dynamics of a fractional predator-prey system with time delay and Allee effect," Chaos, Solitons & Fractals, Elsevier, vol. 162(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. Zhu, Linhe & Liu, Wenshan & Zhang, Zhengdi, 2021. "Interplay between epidemic and information spreading on multiplex networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 268-279.
    2. Zhu, Linhe & Huang, Xiaoyuan, 2021. "Modeling the dynamics of multi-cluster information propagation in presence of time delay," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. 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).
    4. Li, Xiaopeng & Hao, Gang & Zhang, Zhipeng & Xia, Chengyi, 2021. "Evolution of cooperation in heterogeneously stochastic interactions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    5. Deng, Zhenghong & Wang, Shengnan & Gu, Zhiyang & Xu, Juwei & Song, Qun, 2017. "Heterogeneous preference selection promotes cooperation in spatial prisoners’ dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 20-23.
    6. Mbava, W. & Mugisha, J.Y.T. & Gonsalves, J.W., 2017. "Prey, predator and super-predator model with disease in the super-predator," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 92-114.
    7. Wang, Lei & Wang, Juan & Guo, Baohong & Ding, Shuai & Li, Yukun & Xia, Chengyi, 2014. "Effects of benefit-inspired network coevolution on spatial reciprocity in the prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 9-16.
    8. Sakthivel, R. & Joby, Maya & Wang, Chao & Kaviarasan, B., 2018. "Finite-time fault-tolerant control of neutral systems against actuator saturation and nonlinear actuator faults," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 425-436.
    9. Zhang, Jing & Wang, Xiaoli & Xie, Yanxi & Wang, Meihua, 2022. "Research on multi-topic network public opinion propagation model with time delay in emergencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    10. Hu, Menglong & Wang, Juan & Kong, Lingcong & An, Kang & Bi, Tao & Guo, Baohong & Dong, Enzeng, 2015. "Incorporating the information from direct and indirect neighbors into fitness evaluation enhances the cooperation in the social dilemmas," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 47-52.
    11. 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.
    12. 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).
    13. Alatas, Husin & Nurhimawan, Salamet & Asmat, Fikri & Hardhienata, Hendradi, 2017. "Dynamics of an agent-based opinion model with complete social connectivity network," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 24-32.
    14. Dong, Yafang & Huo, Liang'an & Zhao, Laijun, 2022. "An improved two-layer model for rumor propagation considering time delay and event-triggered impulsive control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    15. Lin, Jingyan & Huang, Changwei & Dai, Qionglin & Yang, Junzhong, 2020. "Evolutionary game dynamics of combining the payoff-driven and conformity-driven update rules," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    16. Wang, Xiaofeng & Perc, Matjaž, 2021. "Emergence of cooperation in spatial social dilemmas with expulsion," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    17. Harshavarthini, S. & Sakthivel, R. & Ma, Yong-Ki & Muslim, M., 2020. "Finite-time resilient fault-tolerant investment policy scheme for chaotic nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    18. Li, Xiaopeng & Sun, Shiwen & Xia, Chengyi, 2019. "Reputation-based adaptive adjustment of link weight among individuals promotes the cooperation in spatial social dilemmas," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 810-820.
    19. Shuzhen Yu & Zhiyong Yu & Haijun Jiang, 2022. "Stability, Hopf Bifurcation and Optimal Control of Multilingual Rumor-Spreading Model with Isolation Mechanism," Mathematics, MDPI, vol. 10(23), pages 1-29, December.
    20. Zhou, Tianwei & Ding, Shuai & Fan, Wenjuan & Wang, Hao, 2016. "An improved public goods game model with reputation effect on the spatial lattices," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 130-135.

    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:150:y:2021:i:c:s0960077921004550. 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.