An Investigation on Dynamics and Stability of a Predator-Prey Model with Logistic prey growth and Interspecific Competition

Abstract

 This paper investigates a mathematical analysis of an extended predator- prey model that includes logistic growth for prey population and interspecific competition influencing both species. To incorporate more realistic ecological interaction, the classical Lotka-Volterra model is extended by incorporating a carrying capacity for the prey and competitive terms. The equilibrium point of the extended model is derived and derive stability analysis using linearization and Jacobian matrix. Numerical simulations are performed to demonstrates the dynamic behavior of the system under various initial conditions. This study highlights that including logistic growth and interspecific competition yield a more precise and robust representation of the predator –prey dynamics. This result provides valuable understanding ecological balance and help in managing biological populations in competitive environments.