In this paper, we present an advanced model for Channel State Information (CSI) tracking, leveraging a dynamical system approach to adapt CSI dynamically based on exogenous contextual information. This methodology allows for continuous updates to the Channel Knowledge Map (CKM), enhancing communication reliability and responsiveness in dynamic environments. To generate realistic and comprehensive datasets for training and evaluation, we developed a new MATLAB simulator that models radio wave propagation in urban environments. We address the challenge of real-time CKM adaptation using online learning of the Koopman operator, a technique that forecasts channel behaviour by exploiting dynamical system properties. Our approach supports real-time updates with high accuracy and efficiency, as demonstrated by experiments with varying window sizes for the Koopman Autoencoder model. A window size of 100 was found to offer the best balance between prediction accuracy (RMSE: 1.8323 +- 1.1071, MAE: 0.3780 +- 0.2221) and computational efficiency (training time: 231.1 +- 82.5 ms, prediction time: 109.0 +- 55.7 ms). Additionally, we introduce a moving window mechanism to address privacy and security concerns by updating the Koopman operator within the window and purging input data thereafter, minimising data retention and storage risks. This ensures the CKM remains accurate and relevant while maintaining stringent data privacy standards. Our findings suggest that this approach can significantly improve the resilience and security of communication systems, making them highly adaptable to environmental changes without compromising user privacy.