Many problems in biology, physics and engineering involve predicting and controlling complex systems, loosely defined as interconnected system-of-systems. Such systems can exhibit a variety of interesting non-equilibrium features such as emergence and phase transitions, which result from mutual interactions between nonlinear subsystems.
Modelling these systems is a task in-and-of itself, as systems can span many physical domains and evolve of multiple time scales. Nonetheless, one wishes to analyse the geometry of these models and relate both qualitative and quantitative insights back to the physical system.
Beginning with the modelling and analysis of a coupled optomechanical systems, this talk presents some recent results concerning the existence and stability of emergent oscillations. This forms the basis for a discussion of new directions in symbolic computational techniques for complex physical systems as a means to discuss emergence more generally.
Peter Cudmore is a Postdoctoral Research Fellow in the Systems Biology Lab at University of Melbourne where he is developing and applying multi-physics network modelling techniques to biological systems. A key focus of his research is to understand the geometry of complex systems, and how emergence can be predicted, controlled. Peter completed his B.Sc. and Ph.D. (Applied Mathematics) at the University of Queensland.