Analysis of Four-Species Diffusive and Non-Diffusive Food Chains Using Artificial Neural Networking - Muhammad Shoaib Arif; Ateeq Ur Rehman; Asad Ejaz (Emerging Science Journal)
This study uncovers the findings of a four-species food chain model, focusing on its equilibrium points, global stability, and population dynamics. Through rigorous mathematical analysis, we identify the equilibrium points of the model and investigate the global stability of the coexistence equilibrium point. We present the existence conditions for all equilibrium points and assess the stability characteristics of the coexistence fixed point. Time series solutions offer a captivating perspective on the dynamic behavior of a system. Our investigation into the effects of parameters provides the fluctuations in population density, with specific parameters exerting significant influence as a result of the random movement of linked species. Understanding the need for taking account of diffusion-dominated situations, the diffusive version of the model is developed and analyzed. By constructing a numerical system with three-time levels (n-1, n, and n+1), its stability can potentially be tested thoroughly using the Von Neumann stability criterion. Numerical simulations and graphs depict the system's dynamic interaction. We also examine how diffusion coefficients affect population density, creating remarkable charts that show interactive species relationships. We also identify exciting bifurcation occurrences in the system, which helps us comprehend its complex dynamics. Predator-prey systems can be studied using Artificial Neural Networks (ANNs) to handle complexity, discover patterns, and predict future dynamics. ANNs can predict population dynamics and assess various parameters by analyzing prior data. Their adaptability lets them improve forecasts over time, improving management methods and ecosystem balance. We use ANN methods to see how specific parameters affect interacting species population dynamics.