• Tönu Puu


Quite as in the case of migration the natural setting for business cycles is geographical space of two dimensions. Cycles are never but local phenomena, but spread through trade, import and export, from one location, region, or country to another. So, we can try to again put the model on square lattice, and let each cell have a multiplier-accelerator process of its own, though all the cells are now coupled through neighbourhood effects from adjacent cells. The coupling is easily obtained through a linear import/export propensity as once introduced by L.A. Metzler in 1950. As usual, a generalization in one sense must be compensated through some simplification of something else, as it is so easy to land on models that remain just statements that cannot be analyzed. Therefore we propose to sacrifice the present author’s own model with capital, and to use a Goodwin type model where the floor and ceiling are both integrated in a single investment function with a cubic nonlinearity. There are many issues to study numerically. Like a partial differential equation such a discrete spatial model needs some boundary condition, which may stipulate insulation, trade with the exterior, or even periodic disturbances from the surrounding. Part of the boundary condition is the definition of the shape of the region. As neighbour cells may trigger a cell into prosperity or depression, it is natural if the “game of life” with its eventually moving and flickering flickering cell aggregates comes into mind. However, we must consider that the setting of this square is a topological equivalent to the surface of a torus, and nobody yet lived in a geographical region of torus shape. The author has seen some contributions in this direction, though this is sheer abuse of analogy.


  1. Puu T (1989) Nonlinear economic dynamics. Springer lecture notes in economics and mathematical systems, vol 336. Springer, Berlin, pp 1–119Google Scholar
  2. Puu T, Sushko I (2004) A business cycle model with cubic nonlinearity. Chaos Solitons Fractals 19:597–612CrossRefGoogle Scholar
  3. Sushko I, Puu T, Gardini L (2003) The Hicksian floor–roof model for two regions linked by interregional trade. Chaos Solitons Fractals 18:593–612CrossRefGoogle Scholar

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Authors and Affiliations

  • Tönu Puu
    • 1
  1. 1.Centre for Regional Science (CERUM)Umeå UniversityUmeåSweden

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