Mathematical modeling and stability analysis of ecological species: A review

Mathematical ecology focuses on the interactions between ecological species and their environments, using quantitative tools to understand population dynamics, species interactions, and ecosystem stability. This review provides an overview of key mathematical models that describe these ecological processes, including the classical Lotka- Volterra equations, predator-prey dynamics, and models of competition and mutualism. Particular emphasis is placed on the role of stability analysis in predicting system behaviour, with discussions on both linear and nonlinear techniques. Additionally, the review highlights selected recent developments and applications of these models in resource management and conservation contexts. Rather than claiming an exhaustive compilation of advances, this work aims to outline foundational concepts alongside representative modern contributions to the field.