IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v192y2025ics096007792500030x.html
   My bibliography  Save this article

Effects of mortality on a predator–prey model in crisp, fuzzy, and spatial environments: A dynamical approach

Author

Listed:
  • Shivam,
  • Singh, Teekam
  • Rawat, Shivam
  • Singh, Anupam

Abstract

The dynamic relationship between predators and prey plays a vital role in upholding equilibrium within the natural environment. Mortality plays a crucial role in maintaining the delicate equilibrium of ecosystems. This paper delves into the consequences of mortality in a predator–prey model that incorporates hydra, the Allee effect, and mutual interference among predators. We first established a crisp predator–prey model and then transformed it into a fuzzy model, representing the control parameters as triangular intuitionistic fuzzy numbers. We transform the fuzzy model into the defuzzified model by applying a graded mean integration technique. This technique allows for efficient solution determination using triangular intuitionistic fuzzy numbers. The theoretical section explores the presence and durability of equilibrium points and Hopf bifurcation on mortality parameters. Living organisms have the ability to move from one place to another, so we created a spatial model based on a crisp model. In order to investigate the impact of random movement of species within a population in an isolated area with different mortality parameters, we employ Turing instability. We confirm the theoretical results using the MATLAB package. The phase trajectories for various initial conditions in both environments are displayed, showcasing the species’ population fluctuations. We use the MATCONT package to illustrate the various scenarios that emerge when we alter the mortality parameters. We calculate the presence of saddle–node (SN), Hopf point (H), and Cusp point (CS) in the model. In addition, our spatial model analysis reveals various spatial structures within the isolated domain, including spots, stripes, and mixed patterns. The results indicate that mortality has a beneficial impact on the prey–predator population, helping to sustain ecological balance.

Suggested Citation

  • Shivam, & Singh, Teekam & Rawat, Shivam & Singh, Anupam, 2025. "Effects of mortality on a predator–prey model in crisp, fuzzy, and spatial environments: A dynamical approach," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
  • Handle: RePEc:eee:chsofr:v:192:y:2025:i:c:s096007792500030x
    DOI: 10.1016/j.chaos.2025.116017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792500030X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2025.116017?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.

    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:192:y:2025:i:c:s096007792500030x. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.