Endogenous cycles in discontinuous growth models

Tramontana, Fabio; Gardini, Laura; Agliari, Anna

doi:10.1016/j.matcom.2010.12.002

Cited by 15 publications

(19 citation statements)

References 36 publications

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“…These bifurcation mechanisms are quite important for their role in applied models, in several contexts. In engineering, see [9,[14][15][16]23], but also in economics (see [7,[19][20][21]). …”

Section: Introductionmentioning

confidence: 99%

Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches

et al. 2012

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Abstract. This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where it was proved that in the case of an increasing/decreasing contracting functions on the left/right side of a border point, at such a crossing point, we have a big-bang bifurcation, from which infinitely many border collision bifurcation curves are issuing.AMS (2000) subject classification. 37E05, 37G10, 37G35. Keywords. piecewise smooth maps, border collision bifurcations, organizing centers.Résumé. Cet travail est une contributionà la classification des comportements dynamiques de systèmes réguliers par morceaux dans lesquels les bifurcations de collision au bord caractérisent les changements qualitatifs de la dynamique. Un point central de notreétude est l'intersection de deux courbes de bifurcation de colision au bord dans un plan de paramètre. Ce problème est aussi associé avec la rupture de continuité en un point fixe d'une application régulière par morceaux. Nous allons relacher l'hypothèse requise dans [4], où il aété montré que dans le cas de fonctions contractantes croissantes/décroissantes strictementà gauche/droite d'un point du bord, en un tel point de franchissement, nous avons une bifurcation big-bang, de laquelle est issue une infinité de courbes de bifurcation de collision au bord.Mots clefs. applications régulières par morceaux, bifurcations de collision au bord, centres organisateurs.

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Section: Introductionmentioning

confidence: 99%

Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches

et al. 2012

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“…In order to observe fluctuations and more complex dynamics, map has to be nonmonotonic. Notice that several works (see, among all, Brianzoni et al [8] and Tramontana et al [27]) demonstrate that cycles and chaotic dynamics appear when the ES between production factors is sufficiently low.…”

Section: Proposition 8 Let As Given By ( ) Be Bimodal With Minimum Pmentioning

confidence: 97%

On the Effect of Labour Productivity on Growth: Endogenous Fluctuations and Complex Dynamics

Grassetti

Mammana

Michetti

2018

Discrete Dynamics in Nature and Society

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This paper introduces a sigmoidal production function that considers production possible even when the only input is labour. The long-run behaviour of an economy described by the neoclassical Solow-type growth model with differential savings is investigated considering the technology presented. It is found that labour productivity influences the existence of boom and bust periods as well as the level of capital per capita in equilibrium.

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“…The dynamics of piecewise linear maps with one discontinuity point are well known in the case of slopes all smaller than one in modulus (see Leonov 1959;Leonov 1962;Keener 1980;Avrutin et al 2010;Gardini et al 2010, and applications to economics in Gardini et al 2011;Tramontana et al 2010;Tramontana et al 2011), and this is also relevant to our system. However, our system has two discontinuity points, which can be seen, for example, in Tramontana et al 2011. The restrictions related to the economic significance of the model, lead to equality of two of the three branches of the map, and this particularity allows us a complete characterization of the dynamics of the model.…”

Section: Introductionmentioning

confidence: 94%

A piecewise linear model of credit traps and credit cycles: a complete characterization

Matsuyama

Sushko

Gardini

2018

Decisions Econ Finan

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We reconsider a regime-switching model of credit frictions which has been proposed in a general framework by Matsuyama for the case of Cobb-Douglas production functions. This results in a piecewise linear map with two discontinuity points and all three branches having the same slope. We offer a complete characterization of the bifurcation structure in the parameter space, as well as of the attracting sets and related basins of attraction in the phase space. We also discuss parameter regions associated with overshooting, leapfrogging, poverty traps, reversal of fortune, and growth miracle, as well as cycles with any kind of switching between the expansionary and contractionary phases.

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Endogenous cycles in discontinuous growth models

Cited by 15 publications

References 36 publications

Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches

Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches

On the Effect of Labour Productivity on Growth: Endogenous Fluctuations and Complex Dynamics

A piecewise linear model of credit traps and credit cycles: a complete characterization

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