| 1. |
- Puu, Tönu, 1936-, et al.
(författare)
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A business cycle model with cubic nonlinearity
- 2004
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Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 19:3, s. 597-612
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Tidskriftsartikel (refereegranskat)abstract
- This paper deals with a simple multiplier-accelerator model of the business cycle, including a cubic nonlinearity. The corresponding two dimensional iterative map is represented in terms of its bifurcation diagram in parameter space. A number of bifurcation sequences for attractors and their basins are studied.
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| 2. |
- Puu, Tönu, 1936-, et al.
(författare)
-
Cournot duopoly when the competitors operate under capacity constraints
- 2003
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier. - 0960-0779 .- 1873-2887. ; 18:3, s. 577-592
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Tidskriftsartikel (refereegranskat)abstract
- The paper considers Cournot duopoly where the competitors have capacity constraints. An isoelastic demand function, which always results when consumers maximise utility functions of the Cobb–Douglas type, is used. It has been demonstrated that isoelastic demand, combined with constant marginal costs, results in complex dynamics. The purpose of the present paper is to reconsider the case, using in stead cost functions with capacity limits. This is a point on which Edgeworth insisted as important. Comparisons between cases of few large and many small competitors cannot be made when firms have constant returns and hence are all infinitely large in potential.
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| 3. |
- Sushko, Irina, et al.
(författare)
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The Hicksian floor–roof model for two regions linked by interregional trade
- 2003
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Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 18:3, s. 593-612
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- The Hicksian multiplier–accelerator model with the original floor–roof limits to investments is studied for the case of two regions linked by interregional trade. The result is a piecewise linear continuous four dimensional map, which is reduced to three dimensions through the choice of an appropriate distributed consumption lag. The attractors, basins, and bifurcations of the map are studied under the assumption of a certain symmetry between the regions. The Neimark–Hopf bifurcation for piecewise linear maps is described in detail which gives rise to the appearance of an attracting closed invariant curve homeomorphic to a circle. The structure of resonance regions in the parameter space are investigated.
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| 4. |
- Sushko, Irina, et al.
(författare)
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Tongues of periodicity in a family of two-dimensional discontinuous maps of real Mobius type
- 2004
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 21:2, s. 403-412
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider a two-dimensional piecewise-smooth discontinuous map representing the so-called "relative dynamics" of an Hicksian business cycle model. The main features of the dynamics occur in the parameter region in which no fixed points at finite distance exist, but we may have attracting cycles of any periods. The bifurcations associated with the periodicity tongues of the map are studied making use of the first-return map on a suitable segment of the phase plane. The bifurcation curves bounding the periodicity tongues in the parameter plane are related with saddle-node and border-collision bifurcations of the first-return map. Moreover, the particular "sausages structure" of the bifurcation tongues is also explained.
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| 5. |
- Agliari, Anna, et al.
(författare)
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Global bifurcations of basins in a triopoly game
- 2002
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Ingår i: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - 0218-1274. ; 12:10, s. 2175-2207
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Tidskriftsartikel (refereegranskat)abstract
- A Cournot model based on bounded inverse demand function and constant marginal production costs is studied. The case of three producers is considered and the adjustment process reduces to a three-dimensional noninvertible map in the output of competitors. The analysis of the dynamical behavior of the map is performed by the "critical curve method", extended to the critical surfaces in 3D. By this method, we explain the different bifurcations in the basins of attraction and in the attracting sets. In particular, given the economic application, feasible trajectories are focused, starting from the simple situation of two identical producers and extending the results to the generic case.
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| 6. |
- Agliari, Anna, et al.
(författare)
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The dynamics of a triopoly Cournot game
- 2000
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Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 11:15, s. 2531-2560
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Tidskriftsartikel (refereegranskat)abstract
- This paper reconsiders the Cournot oligopoly (noncooperative) game with iso-elastic demand and constant marginal costs, one of the rare cases where the reaction functions can be derived in closed form. It focuses the case of three competitors, and so also extends the critical line method for non-invertible maps to the study of critical surfaces in 3D. By this method the various bifurcations of the attractors and their basins are studied. As a special case the restriction of the map to an invariant plane when two of the three firms are identical is focused.
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| 7. |
- Gallegati, Mauro, et al.
(författare)
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Hicks’ trade cycle revisited : cycles and bifurcations
- 2003
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Ingår i: Mathematics and Computers in Simulation. - 0378-4754 .- 1872-7166. ; 63:6, s. 505-527
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Tidskriftsartikel (refereegranskat)abstract
- In the Trade Cycle, Hicks introduced the idea that endogenous fluctuations could be coupled with a growth process via nonlinear processes. To argue for this hypothesis, Hicks used a piecewise-linear model. This paper shows the need for a reinterpretation of Hicks’ contribution in the light of a more careful mathematical investigation. In particular, it will be shown that only one bound is needed to have non explosive outcome if the equilibrium point is an unstable focus. It will also be shown that when the fixed point is unstable the attracting set has a particular structure: It is a one-dimensional closed invariant curve, made up of a finite number of linear pieces, on which the dynamics are either periodic or quasi-periodic. The conditions under which the model produces periodic or quasi-periodic trajectories and the related bifurcations as a function of the main economic parameters are determined.
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| 8. |
- Puu, Tönu, 1936-
(författare)
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Bertrand oligopoly revisited
- 2001
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Ingår i: Discrete dynamics in nature and society. - 1026-0226 .- 1607-887X. ; 6:1, s. 1-10
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Tidskriftsartikel (refereegranskat)abstract
- This paper reconsiders Bertrand duopoly and oligopoly in the spatial formulation due to Hotelling, 1929. The equilibrium configurations of price and location structure are considered, given elastic demand, and a full dynamics is formulated in order to check for stability of equilibrium and the possibilities of complex dynamics, such as occurs easily with Cournot oligopoly. The main discussion concerns Hotelling's original case of two sellers on a given interval, though results for different cases, such as three firms on a circle, and lattices in 2D are indicated.
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| 9. |
- Puu, Tönu, 1936-
(författare)
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Hotelling's "ice cream dealers" with elastic demand
- 2002
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Ingår i: The annals of regional science. - : Springer Science and Business Media LLC. - 0570-1864 .- 1432-0592. ; 36:1, s. 1-17
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Tidskriftsartikel (refereegranskat)abstract
- This article reconsiders the Hotelling duopoly model of 1929, but under elastic demand, more precisely a linear demand function. The equilibrium state for identical firms is fully described, and the intervals of different regimes: independent monopolies, genuine duopoly competition, and price cutting wars, are specified in terms of one single compound parameter (maximum price, minus marginal production cost, divided by transportation cost).
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