Positive invariant sets and global exponential attractive sets of a class of neural networks with unbounded time-delays

In this paper, we study the positive invariant sets and global exponential attractive sets for a class of neural networks with unbounded time-delays. Based on the assumption for the activation function satisfying the global Lipschitz condition, several algebraic criterions for the aforementioned sets are obtained by constructing proper Lyapunov functions and employing Young inequality. Finally, examples are given and analyzed to demonstrate our results.

Research highlightsThe time delay investigated here is time-varying and unbounded but not the infinite distributed delays.
► The active functions discussed in our paper are unbounded.
► The detailed estimations for the globally exponentially attractive sets of the researched neural network are derived.