Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays

Abstract

In this paper, the synchronization control problem of high-order quaternion Hopfield neural networks (HOQHNNs) with unbounded distributed delays and time-varying discrete delays is studied. Since the non-exchangeability of quaternion multiplication operation, the error system is first decomposed into equivalent real-valued systems, and then the driving-response structure of HOQHNN is achieved exponential synchronization by designing a state feedback controller. At the same time, two examples are offered to illustrate the applicability of the consequences obtained. Finally, the obtained global exponential synchronization criterion is applied to encrypt and decrypt color images. The method proposed here has four advantages: (1) There is no need to construct any Lyapunov–Krasovskii functional, which is straight in the light of the definition of global exponential synchronization; (2) The obtained synchronization criterion contains only a few simple inequalities, which can find the solutions readily; (3) The proposed method is available to real-valued and complex-valued neural networks; (4) The obtained results are helpful for the image secure transmission.