<p>This article delves into the adaptive global polynomial synchronization (GPS) for a memristive complex-valued neural networks (MCVNNs) with proportional delays through adaptive control. By introducing a polynomial function to design an adaptive controller and construct a new Lyapunov functional, a GPS criterion is derived. Furthermore, instead of introducing polynomial function, a novel lemma which is applicable to proportional delay differential inequality (PDDI) systems is established. And with the aid of this lemma, a GPS criterion is obtained under a simpler adaptive controller. The innovation lies in the establishment of two adaptive controllers and easily verifiable GPS synchronization criteria, as well as the development of a novel lemma applicable to PDDI systems. Compared with the synchronization criteria of previous MCVNNs, the criteria in this article are very concise and practical. Lastly, we validate the derived results through a numerical example. Furthermore, we apply GPS control to image encryption in the example, thereby demonstrating the practicality and effectiveness of the proposed synchronization strategy and encryption algorithm.</p>