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

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation Pub Date : 2025-01-30 DOI:10.1016/j.matcom.2025.01.020

Karima Mokni, Hajar Mouhsine, Mohamed Ch-Chaoui

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引用次数: 0

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.

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来源期刊

Mathematics and Computers in Simulation 数学-计算机：跨学科应用

CiteScore

8.90

自引率

4.30%

发文量

335

审稿时长

54 days

期刊介绍： The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.