1. 
 Canovas, Jose S, et al.
(författare)

Detecting Chaos in a Duopoly Model via Symbolic Dynamics
 2010

Ingår i: Discrete and continuous dynamical systems. Series B.  Springfield, USA : American Institute of Mathematical Sciences.  15313492. ; 13:2, s. 269278

Tidskriftsartikel (refereegranskat)abstract
 This paper considers a Cournot duopoly model assuming isoelastic demand and smooth cost functions with builtin capacity limits. When the firms cannot obtain positive profits they are assumed to choose small "standby" outputs rather than closing down, in order to avoid substantial fitting up costs when market conditions turnout more favorable. It is shown that the model provides chaotic behavior. In particular, the system has positive topological entropy and hence the map is chaotic in the LiYorke sense. Moreover, chaos is not only topological but also physically observable.


2. 
 Puu, Tönu, 1936
(författare)

On the economics of increasing complexity : With some special focus on culture
 2010

Ingår i: Journal of Economic Behavior and Organization.  Elsevier.  01672681. ; 75:1, s. 5968

Tidskriftsartikel (refereegranskat)abstract
 This contribution seeks to find a setting in which evolution in terms of changing structure, rather than growth within a given structure, can be modelled. In particular the evolution of increasing complexity is focused. The setting chosen uses Lancasterian property space as an invariant in which the changing, emerging, and disappearing actual implements are property bundles. The aim is to produce a development tree like the Darwinian, and the tool used for modelling the branching bifurcations is catastrophe theory.


3. 
 Sushko, Iryna, et al.
(författare)

Regular and chaotic growth in a Hicksian Floor/ceiling model
 2010

Ingår i: Journal of Economic Behavior and Organization.  Elsevier.  01672681. ; 75:1, s. 7794

Tidskriftsartikel (refereegranskat)abstract
 In some previous papers the present authors reassembled the Hicksian trade cycle model in a new way. The floor was tied to depreciation on capital, itself the cumulative sum of past net investments, for which the principle of acceleration provided an explanation. Hence no alien elements were needed to include capital, and so close the system. The resulting model created a growth trend along with growth rate cycles, which could be periodic or quasiperiodic. In the current paper, the ceiling, using capital stock as a capacity limit for production, is added. It then turns out that pure growth no longer exists, and chaos and multistability become possible, which they were not in the previous model. A variety of bifurcation scenarios is explored, and a full understanding of the working of the fourpiece, originally threedimensional, piecewise smooth map, is attained, using a reduction to a onedimensional return map.


4. 
 Tramontana, Fabio, et al.
(författare)

Global bifurcations in a piecewisesmooth Cournot duopoly game
 2010

Ingår i: Chaos, Solitons & Fractals.  Oxford : PergamonElsevier Science Ltd.  09600779. ; 43:12, s. 1524

Tidskriftsartikel (refereegranskat)abstract
 The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu [2]. The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the NeimarkSacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties differ significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist. (C) 2010 Elsevier Ltd. All rights reserved.


5. 
 Tramontana, Fabio, et al.
(författare)

Mathematical properties of a combined CournotStackelberg model
 2010

Rapport (övrigt vetenskapligt)abstract
 The object of this work is to perform the global analysis of a new duopoly model which couples the two points of view of Cournot and Stackelberg. The Cournot model is assumed with isoelastic demand function and unit costs. The coupling leads to discontinuous reaction functions, whose bifurcations, mainly border collision bifurcations, are investigates as well as the global structure of the basins of attraction. In particular, new properties are shown, associated with the introduction of horizontal branches, which di¤er significantly when the constant value is zero or positive and small. The good behavior of the model with positive constant is proved, leading to stable cycles of any period.


6. 
 Tramontana, Fabio, et al.
(författare)

Mathematical properties of a discontinuous CournotStackelberg model
 2011

Ingår i: Chaos, Solitons & Fractals.  Oxford : PergamonElsevier Science Ltd.  09600779. ; 44:13, s. 5870

Tidskriftsartikel (refereegranskat)abstract
 The object of this work is to perform the global analysis of a recent duopoly model which couples the two points of view of Cournot and Stackelberg [17,18]. The Cournot model is assumed with isoelastic demand function and unit costs. The coupling leads to discontinuous reaction functions, whose bifurcations, mainly border collision bifurcations, are investigated as well as the global structure of the basins of attraction. In particular, new properties are shown, associated with the introduction of horizontal branches, which differ significantly when the constant value is zero or positive and small. The good behavior of the model with positive constant is proved, leading to stable cycles of any period.


7. 
 Tramontana, Fabio, et al.
(författare)

New properties of the Cournot duopoly with isoelastic demand and constant unit costs
 2010

Rapport (övrigt vetenskapligt)abstract
 The object of the work is to perform the global analysis of the Cournot duopoly model with isoelastic demand function and unit costs, presented in Puu (1991). The bifurcation of the unique Cournot fixed point is established, which is a resonant case of the NeimarkShacker bifurcation. New properties associated with the introduction of horizontal branches are evidenced. These properties di¤er significantly when the constant value is zero or positive and small. The good behavior of the case with positive constant is proved, leading always to positive trajectories. Also when the Cournot fixed point is unstable, stable cycles of any period may exist.

