IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v168y2023ics0960077923000322.html
   My bibliography  Save this article

Cross-diffusion induced Turing patterns on multiplex networks of a predator–prey model

Author

Listed:
  • Song, Mingrui
  • Gao, Shupeng
  • Liu, Chen
  • Bai, Yue
  • Zhang, Lei
  • Xie, Beilong
  • Chang, Lili

Abstract

Predator–prey models have generated growing interest across disciplines ranging from mathematics to ecology. The theory of pattern formation in predator–prey systems organized in monolayer networks has often been investigated, due to its significance in both theoretical advances and practical applications. Here we broaden the theory to the case of multiplex networks, which are easily found in diverse areas, such as neuroscience, social networks, and transportation systems. Moreover, we incorporate the model with cross-diffusion by considering that each specie usually has a specific movement tendency. By carrying on the linear analysis, we get the theoretical Turing instability region and find that the homogeneous fixed point can become unstable due to either the topology of multiplex networks or the cross-diffusion, resulting in various Turing patterns. Furthermore, experimental simulation results are in great agreement with theoretical findings, verifying the theoretical analysis’ validity.

Suggested Citation

  • Song, Mingrui & Gao, Shupeng & Liu, Chen & Bai, Yue & Zhang, Lei & Xie, Beilong & Chang, Lili, 2023. "Cross-diffusion induced Turing patterns on multiplex networks of a predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:chsofr:v:168:y:2023:i:c:s0960077923000322
    DOI: 10.1016/j.chaos.2023.113131
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923000322
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113131?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. 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.
    2. Szolnoki, Attila & Perc, Matjaž, 2023. "Oppressed species can form a winning pair in a multi-species ecosystem," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    3. Kabir, KM Ariful & Kuga, Kazuki & Tanimoto, Jun, 2020. "The impact of information spreading on epidemic vaccination game dynamics in a heterogeneous complex network- A theoretical approach," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. Kabir, K.M. Ariful & Tanimoto, Jun, 2019. "Evolutionary vaccination game approach in metapopulation migration model with information spreading on different graphs," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 41-55.
    5. Malbor Asllani & Joseph D. Challenger & Francesco Saverio Pavone & Leonardo Sacconi & Duccio Fanelli, 2014. "The theory of pattern formation on directed networks," Nature Communications, Nature, vol. 5(1), pages 1-9, December.
    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. Owolabi, Kolade M. & Jain, Sonal, 2023. "Spatial patterns through diffusion-driven instability in modified predator–prey models with chaotic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 174(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. Wang, Mengyao & Pan, Qiuhui & He, Mingfeng, 2020. "The interplay of behaviors and attitudes in public goods game considering environmental investment," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Kabir, KM Ariful & Chowdhury, Atiqur & Tanimoto, Jun, 2021. "An evolutionary game modeling to assess the effect of border enforcement measures and socio-economic cost: Export-importation epidemic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Cui, Guang-Hai & Wang, Zhen & Li, Jun-Li & Jin, Xing & Zhang, Zhi-Wang, 2021. "Influence of precaution and dynamic post-indemnity based insurance policy on controlling the propagation of epidemic security risks in networks," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    4. Kabir, K.M. Ariful, 2021. "How evolutionary game could solve the human vaccine dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Alam, Muntasir & Ida, Yuki & Tanimoto, Jun, 2021. "Abrupt epidemic outbreak could be well tackled by multiple pre-emptive provisions-A game approach considering structured and unstructured populations," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Kabir, K.M. Ariful & Tanimoto, Jun, 2019. "Dynamical behaviors for vaccination can suppress infectious disease – A game theoretical approach," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 229-239.
    7. Zheng, Qianqian & Shen, Jianwei, 2020. "Turing instability induced by random network in FitzHugh-Nagumo model," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    8. Yang, Ryoo Kyung & Park, Junpyo, 2023. "Evolutionary dynamics in the cyclic competition system of seven species: Common cascading dynamics in biodiversity," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. Huang, He & Chen, Yahong & Ma, Yefeng, 2021. "Modeling the competitive diffusions of rumor and knowledge and the impacts on epidemic spreading," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    10. Kulsum, Umma & Alam, Muntasir & Kamrujjaman, Md., 2024. "Modeling and investigating the dilemma of early and delayed vaccination driven by the dynamics of imitation and aspiration," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    11. Yunsheng Deng & Jihui Zhang, 2022. "The choice-decision based on memory and payoff favors cooperation in stag hunt game on interdependent networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(2), pages 1-13, February.
    12. Cencetti, Giulia & Battiston, Federico & Carletti, Timoteo & Fanelli, Duccio, 2020. "Generalized patterns from local and non local reactions," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    13. Kabir, K.M. Ariful & Tanimoto, Jun, 2021. "The role of pairwise nonlinear evolutionary dynamics in the rock–paper–scissors game with noise," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    14. Sakthivel, Rathinasamy & Suveetha, V.T. & Nithya, Venkatesh & Sakthivel, Ramalingam, 2020. "Finite-time fault detection filter design for complex systems with multiple stochastic communication and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    15. Wang, Jianwei & Xu, Wenshu & Chen, Wei & Yu, Fengyuan & He, Jialu, 2021. "Information sharing can suppress the spread of epidemics: Voluntary vaccination game on two-layer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    16. 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.
    17. 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).
    18. Xie, Meiling & Li, Yuhan & Feng, Minyu & Kurths, Jürgen, 2023. "Contact-dependent infection and mobility in the metapopulation SIR model from a birth–death process perspective," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    19. Chen, Yahong & Huang, He, 2022. "Modeling the impacts of contact tracing on an epidemic with asymptomatic infection," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    20. Amaral, Marco A. & Oliveira, Marcelo M. de & Javarone, Marco A., 2021. "An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).

    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:168:y:2023:i:c:s0960077923000322. 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.