Low-Dimensional Nonliear Dynamical Systems as a Tool for Socio-Economic Modelling Yuri Yegorov ∗ 15 July 2004 Abstract The art of mathematical modelling challenges both the complex- ity of real world and analytical tractability. While non-linear dynamic systems have been proved to be a proper tool of modelling in physics which captures the essence of the process, their application in social sciences is still very limited. The interaction between social and natu- ral phenomena clearly escapes rationality trap, as nature cannot be ra- tional. But very often low-dimensional systems can both represent an interesting dynamics and allow for some analytical tractability along with numerical robustness of results. Here two 3-dimensional mod- els of such type will be presented. The first focuses on interaction between economics and nature and shows that Malthusian and neo- classical concepts can represent two extreme cases of more complex dynamical system which is governed only by three non-linear differen- tial equations for population, natural resources and technology. The system is derived using quite standard relationships, but taking part of them from economics and other part from biology. The second model is about the link between urbanization and demographic transition. KEYWORDS: non-linear dynamical system, socio-economic modelling, technology, nature, demography, urbanization. * Address: Institute for Advanced Studies, Vienna, Austria, yegorov@ihs.ac.at. This paper was written for the presentation at the RC33 Sixth International Conference on Social Science Methodology, section “Non-linear modelling”. Its elements have been pre- sented at the 2nd International Meeting on Economic Cycles (UNED-San Pablo CEU, Madrid, Spain, September 2002) and at the 8th Viennese Workshop on Optimal Control, Dynamic Games and Nonlinear dynamics, Vienna, Austria, May 2003. I am grateful to the participants of these conferences that gave me useful comments. 1