The dynamic recommender system realizes the real-time recommendation for users by learning the dynamic interest characteristics, which is especially suitable for the scenarios of rapid transfer of user interests, such as e-commerce and social media. The dynamic recommendation model mainly depends on the user-item history interaction sequence with timestamp, which contains historical records that reflect changes in the true interests of users and the popularity of items. Previous methods usually model interaction sequences to learn the dynamic embedding of users and items. However, these methods can not directly capture the excitation effects of different historical information on the evolution process of both sides of the interaction,i.e., the ability of events to influence the occurrence of another event. In this work, we propose a Dynamic Graph Hawkes Process based on Linear complexity Self-Attention (DGHP-LISA) for dynamic recommender systems, which is a new framework for modeling the dynamic relationship between users and items at the same time. Specifically, DGHP-LISA is built on dynamic graph and uses Hawkes process to capture the excitation effects between events. In addition, we propose a new self-attention with linear complexity to model the time correlation of different historical events and the dynamic correlation between different update mechanisms, which drives more accurate modeling of the evolution process of both sides of the interaction. Extensive experiments on three real-world datasets show that our model achieves consistent improvements over state-of-the-art baselines.