To address the challenges of data privacy protection and heterogeneous data in multi-center collaborative modeling for network intrusion detection, this paper proposes a network intrusion detection model for multi-center privacy-preserving computation based on Mamba, named Federated Learning Intrusion Detection System-Mamba (FLIDS-Mamba). FLIDS-Mamba enables each client to conduct local training on independent heterogeneous datasets, which may differ in dimensionality and exhibit imbalanced class distributions. The proposed aggregation mechanism of federated learning optimizes a global model while protecting client data privacy and enabling collaborative modeling of heterogeneous data. The proposed model incorporates a heterogeneous feature adaptation module and a bidirectional feature extraction module to enhance the capture of sequential features and improve intrusion detection performance. Additionally, we effectively mitigate the issue of sample imbalance by dynamically adjusting the loss contributions of different classes. Experiments on the UNSW-NB15, CIC-IDS2017, NSL-KDD, and CSE-CIC-IDS2018 datasets validate the classification of multiple attack types, achieving nearly 95% weighted accuracy overall and up to 99% on the UNSW-NB15 dataset. The results demonstrate that the FLIDS-Mamba model achieves performance close to centralized learning and outperforms existing heterogeneous federated learning models in heterogeneous environments with diverse client data, showcasing excellent detection capability and generalization performance. It provides a stable and privacy-preserving solution for network intrusion detection.