Almost periodic dynamics for impulsive delay neural networks of a general type on almost periodic time scales

• We improve the concepts of almost periodic time scales introduced in 2014.
• We firstly introduce the concepts of rd-piecewise almost periodic functions on almost periodic time scales.
• Some completely new results of almost periodic solutions for impulsive neural networks are obtained.
• The numerical examples and simulations are given to illustrate these effective results.
• The discrete and continuous analysis of dynamic systems can also be unified well on almost periodic time scales.

In this paper, we improve the new concepts of almost periodic time scales addressed in 2014 to introduce the new concepts of piecewise almost periodic functions. Then we establish some first results for the existence and exponential stability of almost periodic solution for a general type of delay neural networks with impulsive effects. The approaches are based on contraction principle and Gronwall–Bellman’s inequality. In addition, the numerical example and simulations are provided to illustrate our time scale methods are feasible and effective. The obtained results are more general and comprehensive than the results obtained on periodic time scales before.