In the field of natural language processing, structured state space sequence models have emerged as a promising class for sequence prediction. Among these, the Mamba network refines the state space based model to develop the selective state space model which excels at long range sequence prediction with reduced model size and computational complexity compared to the transformer architecture. Machine learning, especially with transformers, has long been plagued with the reliance on large, static datasets that often require repeated training and tuning with large power requirements. This work introduces the Mamba network to a particular domain of multivariate time series prediction, focusing on the propagation of dynamical systems within a low-data environment. Despite using only two training data points, the Mamba network demonstrates impressive accuracy in forecasting multivariate state information in the long-term compared to the traditional long short-term memory sequence models. This is evident in its application to highly nonlinear orbit problems such as the perturbed two-body problem and the circular restricted three-body problem. With improved computational complexity and improved sequence modeling in data-constrained training, the Mamba network can provide online training for long-term dynamical system propagation with potential applications in uncertainty propagation or guidance, navigation, and control systems to enable efficient modeling in the Dynamic Data Driven Applications Systems (DDDAS) paradigm.