Complex behavior in fractional - Order Leslie - Gower prey - Predator model with harvesting

Abstract

This article takes harvesting effects into account, to investigate the qualitative behavior of 2D prey-predator model with Leslie - Gower functional response. Existence and uniqueness of the solutions of the system is examined. The prey population is continuously harvested by an harvesting agency and the rate of harvesting is presumed to be proportional to the prey population. Discrete version of the system is obtained to examine the dynamical behavior of the model. Existence of non-negative equilibrium positions is established and a comprehensive analysis on the local stability of the system is performed. Numerical simulations are illustrated to compliment the analytical outcomes. The system undergoes periodic doubling bifurcation under certain conditions. Time plots, phase portraits, limit cycles, bifurcation diagrams and Lyapunov exponent are helpful to study the dynamics of the system. Finally dependence on initial conditions is discussed. Under the influence of harvesting the prey - predator model exhibits rich complex behaviors.