An impulsive state feedback control model for releasing white-headed langurs in captive to the wild

• We apply the theory of differential equation to protect white-headed langurs.
• An impulsive state feedback control model for white-headed langurs is proposed.
• The model describes the behavior of releasing the langurs in captive to the wild.
• We study the existence and the stability of the system's order-1 periodic solution.
• Population migration and artificial breeding can protect the population effectively.

In this paper, an impulsive state feedback control model for releasing white-headed langurs in captive to the wild is investigated. By using the geometric theory of semi-continuous dynamic system, the method of successor functions and the analogue of the Poincare criterion, it is proved that under certain conditions the system has an order-1 periodic solution with trajectory asymptotical stability, and this periodic solution remains above some critical value. The theoretical results are verified by the numerical simulations. The conclusion is that simultaneously taking the measures of both population migration and artificial breeding can effectively protect wild white-headed langurs, so that the population can continue to survive and can avoid becoming extinct.