Stability, bifurcation analysis, and chaos control of a discrete bioeconomic model

In this paper, we propose a host‐parasitoid model with harvest effort. The existence and stability of a positive fixed point are analyzed. The period‐doubling and Neimark–Sacker bifurcations are studied. These analyses are achieved by applying the normal form of the difference‐algebraic system, bifurcation theory, and center manifold theorem. Furthermore, we apply a state‐delayed feedback control strategy to control the complex dynamics of the proposed model. Numerical examples and simulations are given to verify our findings. Owing to the framework of Nicholson–Bailey host‐parasitoid system, the proposed difference‐algebraic model shows rich dynamics compared with the continuous‐time models.