June 2016 – Course “Qualitative Mathematical Modelling of Complex Systems”

Date: 3 June 2016. Location: ICM-CSIC, Barcelona, Spain. Teacher:  Jeffrey Dambacher (CSIRO)

Qualitative mathematical modelling was introduced as a means to understand and predict the dynamics of complex biological and socio-economic systems. The technique poses the question: if all we know of a system is the general nature of relationships between species and environmental and human variables, but not the precise intensity of these interactions, then what do we know?

It turns out that we know not everything, but quite a lot. Qualitative mathematical modelling describes complex systems through only the sign (0, +, -) of the effect or interaction between variables, and thus can easily include variables and processes that are important, yet difficult to measure.

Calculations of system stability and predictions of perturbation response proceed through analysis of the feedback properties of a system. While model predictions are imprecise, there are nonetheless rigorously derived and readily testable.