IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v175y2023ip1s096007792300913x.html
   My bibliography  Save this article

Detection of Hopf bifurcations induced by pregnancy and maturation delays in a spatial predator–prey model via crossing curves method

Author

Listed:
  • Li, Shuai
  • Huang, Chengdai
  • Song, Xinyu

Abstract

We investigate the stability switches behaviors due to Hopf bifurcations triggered by maturation and pregnancy delays for a diffusive predator–prey model under the joint impacts of fear and Allee effect of predators. We firstly carry out the linear analysis of the proposed model by applying the recently developed crossing curves method to cope with the corresponding characteristic equation incorporating wave number as well as delay-dependent parameters. We then procure the Hopf bifurcation curves through which delays pass, the stability of the associated constant equilibrium can change accordingly. Thereupon, we deduce the normal form regarding Hopf bifurcation and thus clarify its properties. Finally, we present a numerical example and perform some simulations to verify the accuracy of the obtained results. It is shown that both the maturation and pregnancy periods can respectively induce stability switches.

Suggested Citation

  • Li, Shuai & Huang, Chengdai & Song, Xinyu, 2023. "Detection of Hopf bifurcations induced by pregnancy and maturation delays in a spatial predator–prey model via crossing curves method," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s096007792300913x
    DOI: 10.1016/j.chaos.2023.114012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792300913X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114012?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. Pal, Debjit & Kesh, Dipak & Mukherjee, Debasis, 2023. "Qualitative study of cross-diffusion and pattern formation in Leslie–Gower predator–prey model with fear and Allee effects," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Ian W. Renner & David I. Warton, 2013. "Equivalence of MAXENT and Poisson Point Process Models for Species Distribution Modeling in Ecology," Biometrics, The International Biometric Society, vol. 69(1), pages 274-281, March.
    3. Bilazeroğlu, Ş. & Merdan, H., 2021. "Hopf bifurcations in a class of reaction-diffusion equations including two discrete time delays: An algorithm for determining Hopf bifurcation, and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 142(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. Qingyi Cui & Changjin Xu & Wei Ou & Yicheng Pang & Zixin Liu & Peiluan Li & Lingyun Yao, 2023. "Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay," Mathematics, MDPI, vol. 11(23), pages 1-23, November.
    2. Li, Shuai & Cao, Jinde & Liu, Heng & Huang, Chengdai, 2024. "Delay-dependent parameters bifurcation in a fractional neural network via geometric methods," Applied Mathematics and Computation, Elsevier, vol. 478(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. Leandro, Camila & Jay-Robert, Pierre & Mériguet, Bruno & Houard, Xavier & Renner, Ian W., 2020. "Is my sdm good enough? insights from a citizen science dataset in a point process modeling framework," Ecological Modelling, Elsevier, vol. 438(C).
    2. Abdollah Jalilian, 2017. "Modelling and classification of species abundance: a case study in the Barro Colorado Island plot," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2401-2409, October.
    3. Holder, Anna M. & Markarian, Arev & Doyle, Jessie M. & Olson, John R., 2020. "Predicting geographic distributions of fishes in remote stream networks using maximum entropy modeling and landscape characterizations," Ecological Modelling, Elsevier, vol. 433(C).
    4. Martín, Gerardo & Yáñez-Arenas, Carlos & Chiappa-Carrara, Xavier, 2022. "Discrepancies between point process models and environmental envelopes identify the niche centroid – geography configuration," Ecological Modelling, Elsevier, vol. 469(C).
    5. Moreno-Amat, Elena & Mateo, Rubén G. & Nieto-Lugilde, Diego & Morueta-Holme, Naia & Svenning, Jens-Christian & García-Amorena, Ignacio, 2015. "Impact of model complexity on cross-temporal transferability in Maxent species distribution models: An assessment using paleobotanical data," Ecological Modelling, Elsevier, vol. 312(C), pages 308-317.
    6. Halvorsen, Rune & Mazzoni, Sabrina & Dirksen, John Wirkola & Næsset, Erik & Gobakken, Terje & Ohlson, Mikael, 2016. "How important are choice of model selection method and spatial autocorrelation of presence data for distribution modelling by MaxEnt?," Ecological Modelling, Elsevier, vol. 328(C), pages 108-118.
    7. Daniel, Jeffrey & Horrocks, Julie & Umphrey, Gary J., 2018. "Penalized composite likelihoods for inhomogeneous Gibbs point process models," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 104-116.
    8. Jeffrey Daniel & Julie Horrocks & Gary J. Umphrey, 2020. "Efficient Modelling of Presence-Only Species Data via Local Background Sampling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 90-111, March.
    9. Pal, Debjit & Kesh, Dipak & Mukherjee, Debasis, 2024. "Cross-diffusion mediated Spatiotemporal patterns in a predator–prey system with hunting cooperation and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 128-147.
    10. Fern, Rachel R. & Morrison, Michael L. & Wang, Hsiao-Hsuan & Grant, William E. & Campbell, Tyler A., 2019. "Incorporating biotic relationships improves species distribution models: Modeling the temporal influence of competition in conspecific nesting birds," Ecological Modelling, Elsevier, vol. 408(C), pages 1-1.
    11. S. Boussouf & T. Fernández & A. B. Hart, 2023. "Landslide susceptibility mapping using maximum entropy (MaxEnt) and geographically weighted logistic regression (GWLR) models in the Río Aguas catchment (Almería, SE Spain)," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 117(1), pages 207-235, May.
    12. Ricardo A. Correia & Miguel N. Bugalho & Aldina M. A. Franco & Jorge M. Palmeirim, 2018. "Contribution of spatially explicit models to climate change adaptation and mitigation plans for a priority forest habitat," Mitigation and Adaptation Strategies for Global Change, Springer, vol. 23(3), pages 371-386, March.
    13. Wang, Henan & Liu, Ping, 2023. "Pattern dynamics of a predator–prey system with cross-diffusion, Allee effect and generalized Holling IV functional response," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    14. Ma, Xindong & Yu, Yue & Wang, Lifeng, 2021. "Complex mixed-mode vibration types triggered by the pitchfork bifurcation delay in a driven van der Pol-Duffing oscillator," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    15. Wiltshire, Kathryn H & Tanner, Jason E, 2020. "Comparing maximum entropy modelling methods to inform aquaculture site selection for novel seaweed species," Ecological Modelling, Elsevier, vol. 429(C).
    16. Tian, Yuan & Li, Huanmeng & Sun, Kaibiao, 2024. "Complex dynamics of a fishery model: Impact of the triple effects of fear, cooperative hunting and intermittent harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 31-48.
    17. Steen, Bart & Broennimann, Olivier & Maiorano, Luigi & Guisan, Antoine, 2024. "How sensitive are species distribution models to different background point selection strategies? A test with species at various equilibrium levels," Ecological Modelling, Elsevier, vol. 493(C).
    18. Christophe Botella & Alexis Joly & Pascal Monestiez & Pierre Bonnet & François Munoz, 2020. "Bias in presence-only niche models related to sampling effort and species niches: Lessons for background point selection," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-18, May.
    19. Bilazeroğlu, Ş. & Göktepe, S. & Merdan, H., 2023. "Effects of the random walk and the maturation period in a diffusive predator–prey system with two discrete delays," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    20. Chih-Wei Lin & Yu Hong & Weihao Tu & Jinfu Liu, 2022. "Multiperiod Dynamic Programming Algorithm for Optimizing a Nature Reserve," Sustainability, MDPI, vol. 14(6), pages 1-17, March.

    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:175:y:2023:i:p1:s096007792300913x. 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.