In the real world, visual stimuli received by the biological visual system are predominantly dynamic rather than static. A better understanding of how the visual cortex represents movie stimuli could provide deeper insight into the information processing mechanisms of the visual system. Although some progress has been made in modeling neural responses to natural movies with deep neural networks, the visual representations of static and dynamic information under such time-series visual stimuli remain to be further explored. In this work, considering abundant recurrent connections in the mouse visual system, we design a recurrent module based on the hierarchy of the mouse cortex and add it into Deep Spiking Neural Networks, which have been demonstrated to be a more compelling computational model for the visual cortex. Using Time-Series Representational Similarity Analysis, we measure the representational similarity between networks and mouse cortical regions under natural movie stimuli. Subsequently, we conduct a comparison of the representational similarity across recurrent/feedforward networks and image/video training tasks. Trained on the video action recognition task, recurrent SNN achieves the highest representational similarity and significantly outperforms feedforward SNN trained on the same task by 15% and the recurrent SNN trained on the image classification task by 8%. We investigate how static and dynamic representations of SNNs influence the similarity, as a way to explain the importance of these two forms of representations in biological neural coding. Taken together, our work is the first to apply deep recurrent SNNs to model the mouse visual cortex under movie stimuli and we establish that these networks are competent to capture both static and dynamic representations and make contributions to understanding the movie information processing mechanisms of the visual cortex.