Uniformly rd -piecewise almost periodic functions with applications to the analysis of impulsive ΔΔ-dynamic system on time scales

• We introduce some new concepts of uniformly rd-piecewise almost periodic functions on time scales and obtain some properties.
• Some new estimation inequalities and completely new theorems are established on time scales for impulsive dynamic systems.
• Several applications are given to illustrate our feasible results.

In the present work, we introduce two equivalent concepts of uniformly rd  -piecewise almost periodic functions on time scales and their equivalence is proved, based on this, some basic properties of them are obtained. Then, some new criteria of exponential dichotomy are established for homogeneous ΔΔ-dynamic system on time scales. Also, some completely new theorems are established on time scales for impulsive almost periodic dynamic systems such as Favard’s theorem and exponential dichotomy theorem. As applications, we provide a method to obtain an almost periodic solution for a given nonhomogeneous impulsive dynamic system. Furthermore, we introduce an impulsive non-autonomous Nicholson’s blowflies system model with patch structure and multiple nonlinear harvesting terms for which the existence and exponential stability of almost periodic solutions are studied, which shows that our results can be applied feasibly and effectively.