Almost periodic dynamical behaviors for generalized Cohen–Grossberg neural networks with discontinuous activations via differential inclusions

•Delayed CGNN with discontinuous right-hand sides was investigated.•The global exponential stability of almost periodic solution to the system was obtained.•The assumptions on monotonicity of the discontinuous activation has been eliminated.•The restriction condition fi+(ρki)>fi-(ρki) has also been eliminated.

In this paper, we investigate the almost periodic dynamical behaviors for a class of general Cohen–Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and nonsmooth analysis theory with generalized Lyapunov approach, we obtain the existence, uniqueness and global stability of almost periodic solution to the neural networks system. It is worthy to pointed out that, without assuming the boundedness or monotonicity of the discontinuous neuron activation functions, our results will also be valid. Finally, we give some numerical examples to show the applicability and effectiveness of our main results.