IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v143y2021ics0960077920309887.html
   My bibliography  Save this article

Dynamical analysis on a bacteria-phages model with delay and diffusion

Author

Listed:
  • Wang, Jingjing
  • Zheng, Hongchan
  • Jia, Yunfeng

Abstract

Delay and diffusion have important significance in enriching the dynamic behavior of nonlinear dynamical systems. In this paper, we study the effects of delay and diffusion on the dynamics of a bacteria-phages model. By analyzing the stability of equilibria and the existence of Hopf bifurcation, we obtain the following results: (i) Under certain condition, only diffusion cannot contribute to the Turing instability, which is different from the general results that the diffusion can destabilize the model and lead model to produce the Turing instability; (ii) Delay or the combination of diffusion and delay can destabilize the model and lead model to generate the Hopf bifurcation and patterns. Moreover, the formulae for determining the properties of Hopf bifurcation are derived. Numerical simulations are carried out to reveal the effects of delay or the combination of diffusion and delay on the stability and Hopf bifurcation for the model. The results obtained are of significance to predict the coexistence of bacteria and phages and to find the appropriate time to implement the phage therapy.

Suggested Citation

  • Wang, Jingjing & Zheng, Hongchan & Jia, Yunfeng, 2021. "Dynamical analysis on a bacteria-phages model with delay and diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309887
    DOI: 10.1016/j.chaos.2020.110597
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920309887
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110597?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. Jana, Debaldev & Pathak, Rachana & Agarwal, Manju, 2016. "On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 252-273.
    2. Wang, Jingjing & Jia, Yunfeng, 2019. "Analysis on bifurcation and stability of a generalized Gray–Scott chemical reaction model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 528(C).
    3. 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.
    4. Misra, A.K. & Gupta, Alok & Venturino, Ezio, 2016. "Cholera dynamics with Bacteriophage infection: A mathematical study," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 610-621.
    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. 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).
    2. Liang, Yuqin & Jia, Yunfeng, 2022. "Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses," Chaos, Solitons & Fractals, Elsevier, vol. 163(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. Datta, Jyotiska & Jana, Debaldev & Upadhyay, Ranjit Kumar, 2019. "Bifurcation and bio-economic analysis of a prey-generalist predator model with Holling type IV functional response and nonlinear age-selective prey harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 229-235.
    2. Parsamanesh, Mahmood & Erfanian, Majid, 2018. "Global dynamics of an epidemic model with standard incidence rate and vaccination strategy," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 192-199.
    3. Medda, Rakesh & Tiwari, Pankaj Kumar & Pal, Samares, 2024. "Impacts of planktonic components on the dynamics of cholera epidemic: Implications from a mathematical model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 505-526.
    4. 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.
    5. Wenqi Zhang & Dan Jin & Ruizhi Yang, 2023. "Hopf Bifurcation in a Predator–Prey Model with Memory Effect in Predator and Anti-Predator Behaviour in Prey," Mathematics, MDPI, vol. 11(3), pages 1-12, January.
    6. Pal, D. & Samanta, G.P. & Mahapatra, G.S., 2017. "Selective harvesting of two competing fish species in the presence of toxicity with time delay," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 74-93.
    7. Xin Jiang, 2021. "Global Dynamics for an Age-Structured Cholera Infection Model with General Infection Rates," Mathematics, MDPI, vol. 9(23), pages 1-20, November.
    8. Zhenglong Chen & Shunjie Li & Xuebing Zhang, 2022. "Analysis of a Delayed Reaction-Diffusion Predator–Prey System with Fear Effect and Anti-Predator Behaviour," Mathematics, MDPI, vol. 10(18), pages 1-20, September.
    9. Jana, Debaldev & Agrawal, Rashmi & Upadhyay, Ranjit Kumar & Samanta, G.P., 2016. "Ecological dynamics of age selective harvesting of fish population: Maximum sustainable yield and its control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 111-122.
    10. Liao, Shi-Gen & Yi, Shu-Ping, 2021. "Modeling and analyzing knowledge transmission process considering free-riding behavior of knowledge acquisition: A waterborne disease approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    11. Lv, Yunfei & Pei, Yongzhen & Wang, Yong, 2019. "Bifurcations and simulations of two predator–prey models with nonlinear harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 158-170.
    12. Duan, Daifeng & Niu, Ben & Wei, Junjie, 2019. "Hopf-Hopf bifurcation and chaotic attractors in a delayed diffusive predator-prey model with fear effect," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 206-216.
    13. Devi, Sapna & Gupta, Nivedita, 2019. "Effects of inclusion of delay in the imposition of environmental tax on the emission of greenhouse gases," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 41-53.
    14. N. S. N. V. K. Vyshnavi Devi & Debaldev Jana & M. Lakshmanan, 2020. "Interplay Between Reproduction and Age Selective Harvesting Delays of a Single Population Non-Autonomous System," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1857-1891, December.

    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:143:y:2021:i:c:s0960077920309887. 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.