Multi-parameter bifurcations in a discrete Ricker-type predator–prey model with prey immigration

Karima Mokni, Hajar Mouhsine and Mohamed Ch-Chaoui

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 233, issue C, 39-59

Abstract: This study examines a discrete-time prey–predator model featuring a Ricker-type growth function and immigration effects to uncover the dynamics shaping ecosystem stability. Through detailed bifurcation analysis, we identify codimension-one bifurcations, including transcritical, period-doubling, and Neimark–Sacker bifurcations, as well as codimension-two bifurcations involving 1:2, 1:3, and 1:4 resonances. Our results reveal that low immigration rates stabilize the system, ensuring predictable population dynamics, while exceeding critical thresholds induces complex behaviors, such as periodic oscillations and chaos. We numerically analyze the dynamics associated with 1:2, 1:3, and 1:4 resonances, utilizing two-parameter bifurcation diagrams and basins of attraction to illustrate the transitions and stability boundaries. These findings highlight the dual role of immigration in stabilizing and destabilizing ecosystems, offering valuable insights for ecological modeling, management, and conservation strategies.

Keywords: Discrete model; Transcritical bifurcation; Period-doubling bifurcation; Neimark–sacker bifurcation; Resonance 1:2, 1:3, 1:4 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475425000205
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:233:y:2025:i:c:p:39-59

DOI: 10.1016/j.matcom.2025.01.020

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().