<p>In the dynamic analysis of memristive neural networks, most of existing conclusions on stability and synchronization cannot take into account both discrete and continuous cases simultaneously. However, some existing results of introducing time-scales theory can only provide Lagrange synchronization results. In this paper, the Lagrange exponential stability and the synchronization of memristive neural networks (MNNs) on time scales are considered. Firstly, the Lagrange exponential stability theory of MNNs is established by means of two-modal analysis. Secondly, a new scale-limited Halanay inequality lemma is constructed to research the synchronization control of the driving-response MNNs in the time-scale domain. Finally, a unified time-scale dynamic analysis tool set is developed, which can deal with the stability and synchronization problems under mixed time scales. Some examples are presented to demonstrate the effectiveness of the theorems, which are subsequently applied to the encryption and decryption of images.</p>