Pullback attractor for neutral Hopfield neural networks with time delay in the leakage term and mixed time delays

In this paper the problem of pullback attractor of neutral Hopfield NNs with mixed time delays and time delay in the leakage term is considered. Based on the Lyapunov–Krasovskii functional method, the theory of pullback attractors and the linear matrix inequalities (LMIs) techniques, some sufficient conditions are established to ensure the existence of the pullback attractor. These conditions are given in terms of LMIs and can be easily numerically checked. Finally, a numerical example is given to appear the effectiveness of our main results.