Stability and bifurcation analysis in a discrete-time logistic model under harvested and feedback control

We discuss a discrete-time logistic model with harvesting and feedback control. The discrete model is obtained by applying Euler’s method to its continuous model. We first determine the equilibrium points, including their existence conditions and their local stability properties. We then apply the central manifold theorem and bifurcation theory to establish conditions for the existence of both period-doubling bifurcation and Neimark-Sacker bifurcation around the positive equilibrium point. Finally, we provide some numerical simulations to verify the feasibility of the theoretical results and demonstrate the complex dynamic behavior. Moreover, the presence of chaos in the system is justified numerically by the computed maximum Lyapunov exponent.