The combination of edge computing and replication technology provides service guarantee for edge applications. However, optimizing replica creation and placement to enhance system performance is challenging due to the limited resources available at the edge. In this context, effective replica management becomes crucial for efficient and reliable edge computing. This study proposes a real-time dynamic replica management model to address the challenges of replica creation and placement in the edge computing environment. Firstly, we design a prediction-based dynamic proactive replica creation algorithm. This algorithm integrates data popularity and node load, utilizing fuzzy membership functions to model data and node states, effectively handling the state uncertainty in certain conditions. It also defines overheating and undercooling similarities to assess the trend of state changes, thereby determining the optimal timing for replica creation. To prevent latency in replica creation, the algorithm employs an Long Short-Term Memory (LSTM) model with a deviation feedback mechanism, which helps prevent lag in replica creation and minimizes unnecessary replica generation. Secondly, we formula replica placement as a multi-objective optimization problem considering the node load and access degree. We use a joint optimization replica placement algorithm that combines Evolutionary Gradient Search (EGS) and Sorting Genetic Algorithm-II to solve the multi-objective replica placement problem. Finally, we conduct extensive experiments on the replica management model. The results demonstrate significant improvements in average response time, effective network utilization rate, storage space utilization rate, and system load balancing, which validate the effectiveness of the proposed method.