This emerging cross-disciplinary field of research incorporates the use and development of nonlinear mathematical modelling, analysis and simulation techniques to provide identification and novel control of previously intractable problems or development of applications over a wide variety of industries. Of particular interest is the occurrence of instabilities which often cannot be predicted using standard linear techniques but are of increasing practical significance. The specific areas of focus and applications of this research include, rolling mill chatter (vibration), rail corrugation, satellite attitude instabilities and the modelling of dynamical phenomena in biological systems such cardiac arrythmia and epileptic seizure and applications using chaotic dynamics. The diversity of application in this field arises because nonlinear phenomena are not restricted to a specific physical model in one area of science but rather emerges from the mathematics behind a system itself; namely nonlinearity. In the case of spacecraft systems such as satellites, nonlinear instabilities result in fluctuations in attitude which may violate highly accurate orientation requirements for communication. In the case of rolling mills, vibration instabilities, known as chatter, result in rejected product, strip breaks, production delays and restriction of mill throughput. Similarly, rail corrugation restricts locomotive speed and results in high maintenance costs and in the extreme cases, derailment. Conversely, recent research indicates that instability behaviour is desirable and has been deliberately designed into biological systems in order that the system may be sensitive to small changes in the environment. As an example, evidence of chaotic dynamics has been identified in the cardiac and neural systems of the human body and has surprisingly been associated with normal healthy functioning.