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In nature, a biological invasion is a common phenomenon that often threatens the existence of local species. Getting rid of the invasive species is hard to achieve after its survival and reproduction. At present, killing some invasive ones and putting artificial local species are usual methods to prevent local species from extinction. An ODE model is constructed to simulate the invasive procedure, and the protection policy is depicted as a series of impulses depending on the state of the variables. Both the ODEs and the impulses form a state feedback impulsive model which describes the invasion and protection together. The existence of homoclinic cycle and bifurcation of order-1 periodic solution of the impulsive model are discussed, and the orbitally asymptotical stability of the order-1 periodic solution is certificated with a novel method. Finally, the numerical simulation result is listed to confirm the theoretical work.

A Research on Nonendangered Population Protection Facing Biological Invasion