  This chapter is about Complexity and Spatial Dynamics in Urban Systems.
Strong inequalities in the size of cities and the apparent difficulty of
limiting their growth raise practical issues for spatial planning. At a time
when new constraints in terms of limited energy and raw material resources or
possible catastrophic events such as pandemics are challenging further urban
expansion, it is important to consolidate the theories from various scientific
disciplines to estimate to what extent the urban dynamics can be modified.
While briefly reviewing the contributions to urban theories provided by the new
developments in complexity sciences, we first advocate for the soundness of
urban theories. Second, we develop our original approach considering spatial
interaction and evolutionary path dependence as major features in the general
behavior of urban entities. Third, we test these principles grounded in an
evolutionary theory of urban systems by experimenting four dynamic models of
urban growth calibrated on harmonized empirical data sets with comparisons
across the whole world.
