JOURNAL ARTICLE

Codimension-1 and Codimension-2 Bifurcations Analysis of Discrete Predator–Prey Model with Herd Behavior.

  • Published In: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2025, v. 35, n. 1. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Li, Wei; Zhang, Chunrui 3 of 3

Abstract

The herd behavior of prey plays an important role in the predator–prey system. In this paper, we analyze the dynamical properties of a discrete predator–prey model with herd behavior. We found that due to the introduction of herd effects, this model exhibits complex dynamical behavior such as codimension-1 bifurcation (Flip and Neimark–Sacker bifurcations) and codimension-2 bifurcation (1:2, 1:3, and 1:4 strong resonance). Using the center manifold theorem and normal form theory, we obtained the critical conditions that may lead to changes in the stability of the system and even the emergence of new stable states or oscillating behaviors. Numerical simulations not only validate theoretical proofs but also reveal the complex and rich dynamical behavior of the discrete model. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. 2025/01, Vol. 35, Issue 1, p1
  • Document Type:Article
  • Subject Area:Environmental Sciences
  • Publication Date:2025
  • ISSN:0218-1274
  • DOI:10.1142/S0218127425500105
  • Accession Number:182482383
  • Copyright Statement:Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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