Almost periodic solutions of quaternion-valued neutral type high-order Hopfield neural networks with state-dependent delays and leakage delays

Abstract

In this paper, we consider the existence and global exponential stability of almost periodic solutions for a class of quaternion-valued neutral type neural networks with state-dependent delays and leakage delays by a direct approach. That is, without decomposing the considered quaternion-valued systems into real-valued systems, by using the contraction mapping fixed point theorem, we obtain the existence of almost periodic solutions of the considered networks with state-dependent delays and leakage delays, and by the counter-evidence method, we obtain the global exponential stability of almost periodic solutions of the considered networks with discrete delays and leakage delays. When the time delays in the considered systems are proportional time delays, our existence results are still true. At the same time, when the considered systems degenerate into real-valued or complex-valued systems, our results are still new.