Multiple positive almost periodic solutions to an impulsive non-autonomous Lotka–Volterra predator–prey system with harvesting terms

• We study an impulsive Lotka–Volterra predator–prey system with harvesting terms.
• Multiplicity of positive almost periodic solutions to the model is obtained.
• Our methods can be used to study other types of population models.

In this paper, by using Mawhin’s continuation theorem of coincidence degree theory, we study an impulsive non-autonomous Lotka–Volterra predator–prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive almost periodic solutions for the system under consideration. Our results of this paper are completely new and our method used in this paper can be used to study the existence of multiple positive almost periodic solutions to other types of population systems.