The mathematics of complex systems

Systems may be complex because their structures are complex, or because their dynamics are so. Extreme sensitivity to initial conditions is a fundamental characteristic of chaos and frustrates our ability to make accurate predictions, though dynamical systems theory can be used in ecological and evolutionary data sets to retrieve the deterministic relations underlying observed relations. Fractals represent another area of complex systems research, directing attention towards the significance of scale: self-similarity across a range of scales may be a property of many ecological processes. Without regularities we have no basis for extrapolating from one system or from one scale to another. Ecosystem experiments can elucidate these issues by providing information simultaneously on multiple scales. Effects can cascade from larger to smaller scales. A central issue is the extent to which the system is driven by external forces and how far its dynamics are autonomous. -P.J.Jarvis