Study on State Feedback Impulsive Control of Red Squirrel Protection with the Influence of Herpes Virus

A kind of state feedback nonlinear impulse model was established to describe the inter-specific competition between red squirrel and grey squirrel and the artificial protection of red squirrel.The effects of releasing artificial red squirrel individuals and eliminating grey individuals on the persistence of red squirrel population were studied. The existence and stability of the order-1 periodic solution of the impulsive control model was proved by using the method of successor function and Dulac function. The numerical simulation is given to verify the theoretical results.