Karima Mokni , Halima Ben Ali , Bapan Ghosh , Mohamed Ch-Chaoui
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Nonlinear dynamics of a Darwinian Ricker system with strong Allee effect and immigration
In this paper, we investigate the complex dynamics of a Darwinian Ricker system through a comprehensive qualitative and dynamical analysis. Our research shows that the system exhibits Neimark–Sacker bifurcation, period-doubling bifurcation, and codimension-two bifurcations associated with 1:2, 1:3, and 1:4 resonances. These findings are derived using bifurcation and center manifold theories. We numerically illustrate all bifurcation results and chaotic features, providing a thorough understanding of the system’s behavior. This detailed examination of the Darwinian Ricker system, with a focus on the interplay between immigration and the strong Allee effect, enhances our understanding of the intricate mechanisms driving population dynamics. Furthermore, it highlights the significant implications for ecological modeling, particularly in predicting ecosystem responses to external perturbations such as climate change and species invasions.
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.