Throughout recent times, cybersecurity problems have occurred in various business applications. Although previous researchers proposed to cope with the occurrence of cybersecurity issues, their methods repeatedly replicated the training processes for several times to classify datasets of these problems in streaming non-stationary environments. In dynamic environments, the conventional methods possibly deteriorate the adaptive solution to prevent these issues. This research proposes a one-pass-throw-away learning using the dynamical structure of the network to solve these problems in dynamic environments. Furthermore, to speed up the computational time and to maintain a minimum space complexity for streaming data, the new concepts of learning in forms of recursive functions were introduced. The information gain-based feature selection was also applied to reduce the learning time during the training process. The experimental results signified that the proposed algorithm outperformed the others in incremental-like and online ensemble learning algorithms in terms of classification accuracy, space complexity, and computational time.