Homoclinic bifurcation of a state feedback impulsive controlled prey–predator system with Holling-II functional response

Keeping ecological balance between prey and predator population in ocean fishery is of great importance in fishery. A free developed two species prey–predator model with Holling-II functional response is carried out, and its fine case equilibrium is discussed. Then, the state feedback model which assumes the harvest of predator and supplement of prey as impulsive disturbance is presented to find the dynamical balance between prey and predator population. The existence of homoclinic cycle and order-1 periodic solution and the orbital asymptotical stability of the order-1 periodic solution are proved. Finally, some numerical simulations are displayed to confirm the results obtained in the paper.