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Abstract

This study explores the idea of stability analysis by using Lyapunov functions in discrete time population models; this work focuses on the nth generation. Further, this investigation aims to extend global stability concepts to discrete-time models and considers the influence of the Allee effect on population dynamics. Mathematical formulations and specific modelling approaches are utilized to investigate the behavior of the population system. The results reveal a larger range of stability in comparison to previous findings, emphasizing the effectiveness of the Lyapunov function approach. Specifically highlighted here are the extension of global stability concepts to the nth generation providing insights into how the Allee effect impacts the stability of discrete time population models. Also, the next-generation results confirm an augmented stability region. A key contribution of the research lies in its exploration of stability concepts beyond the traditional scope, particularly extending to the nth generation. The Allee effect adds novelty to the analysis and provides a more nuanced understanding of population dynamics in discrete time models. This study’s findings have potential applications in various fields, including ecology and population management. Understanding the extended stability concepts in discrete time models can offer insights into the long-term behavior of populations, aiding in more effective conservation strategies.

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