Mathematical Simulations and Analysis of Predator and Prey Model Dynamics with its Functional Response in Ecological Systems

Abstract

The scope of this research includes the development of mathematical models, simulation and Analysis of Prey Model Dynamics with its functional response in an ecological system. The simulation results showed that the functional response affects the dynamics of prey and predator population in the presence of human disturbance with a monotone decrease in the population of the prey; the dynamics of the system led to cycles of predator-prey interactions with human action, demonstrating the classical predator-prey relationship; the noise contributes to the irregularities in the population dynamics thereby making the simulation more realistic and accounting for external factors that may influence the populations; the periodic force introduced oscillations or variations in the predator-prey populations over time and there is a phase shift continuum as the predator population grows and decline, allowing the prey population to recover as a result of the functional response present in the ecological system. Finally, the recommends the optimization of functional response and human disturbance, adaptive management of the ecosystem, advocates incorporating environmental data into numerical models for better dynamism, a collaboration between ecologists, mathematicians, and environmental scientists for better understanding of inter-plays and conduct educational outreaches to raise awareness about the importance of functional response and human action in ecological systems.