Mathematical analysis of a predator-prey system with shared resource, climatic effects, and neural network insight

Abstract

This research paper introduces a predator-prey system in which both organisms depend on a common sustenance source. In order to establish environmental dynamics that are more plausible, we integrated climatic effects on the predator population by implementing a sigmoidal function. The objective is to study the impact of climate on the population dynamics of interacting species by employing mathematical tools like stability analysis and Artificial Neural Networks. By employing meticulous mathematical analysis, we were able to ascertain the equilibrium points of the system and examine their stability on a global scale. Our investigation covered both diffusive and non-diffusive models, providing insight into the unique dynamical characteristics of each. Moreover, in order to leverage the capabilities of modern computational methods, a neural network strategy was implemented to analyses the system's complexities in greater detail. In conclusion, exhaustive diagrams were used to meticulously illustrate the effect of varying parameters, thereby providing invaluable insights into the behavior of the system under various conditions.