Abegye, Shehu Yakubu.2023-12-142023-12-142017-06A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT FOR THE REQUIREMENTS FOR THE AWARD OF THE DEGREE OF MASTER OF SCIENCE (M.SC) IN MATHEMATICS OF THE SCHOOL OF POSTGRADUATE STUDIES, NASARAWA STATE UNIVERSITY, KEFFI.https://keffi.nsuk.edu.ng/handle/20.500.14448/5787A two prey harvesting of Type II functional response of prey species model was proposed. The model was used to study the behaviors of ecological dynamics of Antelope – Zebra – Lion in the tropic. The stability of the equilibrium points of the system was then studied. The analysis shows that without harvesting the system can still co – exist which is showed with increase in population density of the prey species. The two prey can co – exist without the predator for very small inter – specific competition among the prey and shows that the dynamics are globally asymptotically stable. Both the qualitative and numerical analysis of the model indicated that if the harvesting rate of both Antelope and Zebra exceeds their intrinsic growth rate, their population densities would decline to extinction with time. The conditions for global stability of the system was derived using a Lyapunov function. The possibility of existence of the predator – prey system equilibrium was discussed. The numerical simulation of the model portrait that at low predator’s efficiency rate the predator decreases with increase in the population density of the prey species. Furthermore, a decrease in a specie intrinsic growth rate reduces the specie population and the population density of the predator specie will decrease. Also, when the capture rate is zero the prey population increases to its maximum population as the predator goes to extinction and on the other hand with high capture rate the prey suffers till extinction.enThesis