A method for monitoring a dynamic system includes generating system measurement data substantially representative of at least one measured attribute of a plurality of attributes of a dynamic system using at least one measurement device and generating a Poincare map based on the system measurement data. The Poincare map includes representations of the plurality of attributes of the dynamic system. The method also includes determining at least one value for a first attribute of the plurality of attributes of the dynamic system based on the generated Poincare map and regulating real-time operation of the dynamic system based at least partially on the at least one determined value of the first attribute.