Federated Learning (FL) is a collaborative machine learning framework that enables model training using private client data while ensuring privacy protection. Differential Privacy (DP) further strengthens this safeguard, preventing privacy leaks during training. Most existing FL methods that incorporate DP adopt a static privacy budget strategy. However, this approach lacks flexibility and reduces model performance and efficiency. Some researchers have introduced methods for dynamically adjusting privacy budgets. However, these methods often perform poorly in non-independent and identically distributed (NON-IID) scenarios due to insufficient consideration of data imbalance and client performance differences. To address these challenges, this paper proposes a Federated Learning with Dynamic Personalized Differential Privacy algorithm, FL(DP) \(^2\) First, Rényi entropy is utilized to initialize personalized privacy budgets. Second, the privacy budgets are dynamically adjusted using a reward factor. Finally, personalized maximum and minimum privacy budget limits are set based on a chi-squared distribution to maintain consistency with the initial client measurements. Extensive experimental evaluations on real-world NON-IID datasets confirm that FL(DP) \(^2\) performs satisfactorily.