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| 2. |
- Puu, Tönu, 1936-
(författare)
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Chaos in business cycles
- 1991
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 1:5, s. 457-473
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Tidskriftsartikel (refereegranskat)abstract
- The business cycle is studied in terms of the mapping Zt = λZt−1 − (λ+1)Z3t−1 − σYt−1 Yt = Zt−1 + Y−1 where the variables Y, Z denote income and rate of income change respectively, and λ, σ are two structural parameters. The model produces chaotic or periodic output for income differences. For small σ income acts as a slow feed back causing bifurcations between periodic and chaotic behaviour over the cycle. Typically, transitions between prosperity and depression set in with chaos after which there follows a period halving route to order.
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| 3. |
- Puu, Tönu, 1936-
(författare)
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Chaos in duopoly pricing
- 1991
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Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 1:6, s. 573-581
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Tidskriftsartikel (refereegranskat)abstract
- The dynamics of two competing firms in a market is studied in terms of Cournot's duopoly theory. Assuming iso-elastic demand and constant unit production costs the iterative mapping for the outputs of the two firms ensues. The two constants are the unit production costs. The fixed point, the Cournot equilibrium, has earlier been assumed to be the only interesting feature of this model. It is, however, shown that the model can produce persistent motion, periodic or chaotic.
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| 4. |
- Puu, Tönu, 1936-
(författare)
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Hotelling's migration model revisited
- 1991
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Ingår i: Environment and planning A. - 0308-518X .- 1472-3409. ; 23:8, s. 1209-1216
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Tidskriftsartikel (refereegranskat)abstract
- In the present article Hotelling's model of population growth and migration of 1921 is 'revisited'. After a discussion of the stationary solutions and their stability the main point is made. The model itself is structurally unstable, but can be easily stabilized by adding a simple autonomous migration component. By this, the solution curves, in the shape of constant amplitude population waves over space for the original model, either become damped in one direction and explosive in another or are replaced by just one single spatial limit cycle.
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| 5. |
- Puu, Tönu, 1936-
(författare)
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On progress and perfection in the arts
- 1992
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Ingår i: Research in Economics. - : Elsevier. - 1090-9443 .- 1090-9451. ; 46, s. 75-90
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Tidskriftsartikel (refereegranskat)
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| 6. |
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| 7. |
- Puu, Tönu, 1936-
(författare)
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Order and disorder in business cycles
- 1992
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Ingår i: Annals of Operations Research. - : Springer-Verlag. - 0254-5330 .- 1572-9338. ; 37:1, s. 169-183
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that a very simple business cycle model of the multiplier-accelerator type can produce chaotic motion. The model uses a cubic approximation of the nonlinear floor-roof type of investment function, and a two-period distributed lag for consumption. It can be cast as a cubic iterative map for income differences, so that chaotic motion for the differences results in Brownian random walk for income itself. The case can be analyzed by means similar to those used in the study of the iterated quadratic mapping. The cubic, except being based on economic principles, has the advantage over the quadratic that it produces cyclical change. In the fast process for income differences the slowly moving income itself becomes a parameter responsible for feedback causing bifurcations between chaotic and ordered behaviour.
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| 8. |
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| 9. |
- Puu, Tönu, 1936-
(författare)
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Pattern formation in spatial economics
- 1993
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Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 3:1, s. 99-129
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Tidskriftsartikel (refereegranskat)abstract
- A market economy, extended in continuous two-dimensional space, defined by the differential equations: is studied, where φ denotes the vector field of traded commodities, λ the scalar field of commodity prices, q the scalar field of excess supply over demand, and k the cost of transportation. The generic theory of differential equations is used to topologically characterize those patterns that are structurally stable, and the transitions among them are then studied by the elliptic and hyperbolic umblic catastrophes.
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| 10. |
- Rosser, J. Barkley, et al.
(författare)
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Discontinuous change in multilevel hierarchical systems
- 1994
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Ingår i: Systems Research and Behavioral Science (Systems Research). - : John Wiley & Sons Ltd. - 1092-7026. - 9781840649895 ; 11:3, s. 77-93
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Tidskriftsartikel (refereegranskat)abstract
- We examine sources and dynamics of discontinuous changes in discrete multi-level hierarchical ecological-economic systems. We hypothesize the anagenetic moment, the creation of a new level of hierarchy, as arising from variable entrainment at some level. Bottom-up as well as top-down dynamics are studied and competing theories of the sources of such discontinuities are reviewed. Implications for the analysis of complex ecological-economic systems are considered depending on whether they are characterized by single hierarchy, bi-hierarchy, or matrix hierarchy relationships.
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