Existence and exponential stability of the unique positive almost periodic solution for impulsive Nicholson’s blowflies model with linear harvesting term

In this paper, we study an impulsive almost periodic Nicholson’s blowflies model with linear harvesting term. Sufficient conditions are established for the existence of unique almost periodic positive solution by means of the contraction mapping principle. By applying the Liapunov functional, we derive the exponential stability of the almost periodic positive solution. Under the impulsive almost periodic case, we solve an open problem proposed by Berezansky (2010).