Existence and exponential stability of piecewise mean-square almost periodic solutions for impulsive stochastic Nicholson’s blowflies model on time scales

• The concept of piecewise mean-square almost periodic stochastic process is introduced.
• A new impulsive stochastic Nicholsons blowflies model is introduced and studied on time scales.
• The first results of the piecewise mean-square almost periodic solutions for the model are obtained.

In this paper, a class of impulsive stochastic Nicholson’s blowflies model with patch structure and nonlinear harvesting terms is introduced and studied on time scales. By using contraction mapping principal and Gronwall–Bellman inequality technique, some sufficient conditions for the existence and exponential stability of piecewise mean-square almost periodic solutions for the model with infinite delays are established on time scales. Finally, an example is given to demonstrate the validity of the conditions of the main theorem.