Global Lagrange stability for neutral-type Cohen–Grossberg BAM neural networks with mixed time-varying delays

• We study Lagrange stability for Cohen–Grossberg BAM neural networks of neutral-type.
• The delays are multiple time-varying bound or unbound and finite distributed delays.
• Establishing a new differential integral inequality.
• Giving the detail estimations of ultimate boundedness and global attractive sets.
• The results here generalize and improve the earlier publications.

The paper discusses global Lagrange stability for a class of Cohen–Grossberg BAM neural networks of neutral-type with multiple time-varying and finite distributed delays by constructing appropriate Lyapunov-like functions. To this end, we first establish a new differential integral inequality for non-autonomous Cohen–Grossberg BAM neural networks with finite distributed delays. By using the new inequality and employing some other inequality techniques, we analyze two different types of activation functions which include both bounded and unbounded activation functions. Some easily verifiable criteria are obtained for global exponential attractive sets in which all trajectories converge. These results can also be applied to analyze monostable as well as multistable and more extensive neural networks due to making no assumptions on the number of equilibria. Meanwhile, the results obtained in this paper are more general and challenging than that of the existing references. Finally, some examples with numerical simulations are given and analyzed to verify our results.