A Study on Complex Dynamics of Four-Species Fractional Food Web Model With Chaos And Bifurcation

This research examines a food web model to explore the impact of fear effects and harvesting of apex predators on dynamic behaviours. We utilized Caputo and Caputo-Fabrizio (C-F) fractional derivatives to analyze the model's complexity and dynamics. We investigated the existence and uniqueness of solutions through fixed point theory and evaluated the system's stability utilizing the Ulam-Hyers (U-H) criterion. We additionally utilized numerical methods using the Caputo and C-F fractional operators to enhance our comprehension of the food web model. The system analysis demonstrates chaotic dynamics, attractors, and periodic windows. Additionally, we performed numerical simulations in MATLAB to generate more intricate and thorough representations of the food web model, demonstrating the solution's sensitivity to inaccuracies. We examine the time series graph while vary ing the values of the parameters. Significantly, we analyze that the fear effect can mitigate variations in population density, aiding in stabilizing the system.