This paper addresses the issue of economic development from the perspective of productivity increases generated by technological progress emerging from R&D expenditures. The long-run evolutionary path of spatial systems (countries, regions, cities etc.) is analyzed by means of a multi-regional dynamic (discrete-time) model incorporating the spatial transfer of technological change. While a positive feedback exists between R&D and economic growth, the production of new technology itself exhibits decreasing returns. Moreover, capacity constraints also limit growth. The stability conditions associated with R&D and innovation diffusion are extensively studied. It will be demonstrated that the system concerned can generate a wide range of dynamic behaviour, including chaotic evolutions of the May-type. Simulations illustrate this. For example, economic fluctuations can be amplified through innovation diffusion.