Dynamics of sustainable fisheries: a mathematical approach using Lotka-Volterra equations

This study delves into the intricate dynamics of sustainable fisheries through the lens of mathematical modeling, specifically employing the Lotka-Volterra equa-tions. The Lotka-Volterra equations, originally conceived to understand predator-prey interactions, offer a potent framework to model and predict fish population dynamics within aquatic ecosystems. The aim of this research is to demonstrate the applicability and efficacy of the Lotka-Volterra equations in understanding the delicate balance of fish populations and aiding sustainable fisheries man-agement. Through this mathematical approach, we seek to provide a structured methodology and present results that showcase the potential of this model in pre-dicting and managing fish populations. In our analysis, we adjust the parameters of the Lotka-Volterra equations to simulate various scenarios, enabling a compre-hensive understanding of sustainable fishing practices. Our findings underscore the significance of mathematical models, particularly the Lotka-Volterra equa-tions, in informing strategies to maintain fish populations in a sustainable and ecologically balanced manner, thereby ensuring the longevity of marine ecosys-tems and the fisheries that rely upon them.Keywords: Runge-Kutta, Two-step, Exponentially-fitted, Periodic; Oscillatory;