Business Cycle Theory

Gabisch, Günter; Lorenz, Hans-Walter

doi:10.1007/978-3-662-01178-2

Cited by 48 publications

(12 citation statements)

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“…As Gabisch and Lorenz (1987) have pointed out, the flat portion of the Phillips curve constitutes the essential cycle-generating ingredient in this model. For example, suppose that initially the economy is in a state of low employment: "Wages are falling and if the expected demand prices do not fall faster than wages, the real wage declines, implying a rising rate of profit and a rising labor-capital ratio.…”

Section: Nonlinearities and The Labor Marketmentioning

confidence: 93%

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The Labor Market and Business Cycle Theories

Ferri

Greenberg

1989

Lecture Notes in Economics and Mathematical Systems

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Section: Nonlinearities and The Labor Marketmentioning

confidence: 93%

“…As Gabisch-Lorenz (1987) have pointed out: "An inspection of the multiplier reveals that, among other things, the partial derivative Ix, i.e. As Gabisch-Lorenz (1987) have pointed out: "An inspection of the multiplier reveals that, among other things, the partial derivative Ix, i.e.…”

Section: A Limit Cycle In Wages and Employmentmentioning

confidence: 99%

The Labor Market and Business Cycle Theories

Ferri

Greenberg

1989

Lecture Notes in Economics and Mathematical Systems

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“…Economic models, which are based on the van der Pol equation, are considered as prototypes of model for complex economic dynamics [69,70]. Nonlinear dynamic models are used to explain irregular and chaotic behavior of complex economic and financial processes (for example, see the business cycle theory [71,72], nonlinear economic dynamics and chaos [73,74], and stabilization [75]). Some models of business cycles, which are based on the Kaldor nonlinear investment-savings functions [69][70][71][72] and the Goodwin nonlinear accelerator-multiplier (for example, see the Goodwin's paper [76], and [77][78][79]), can be reduced to the van der Pol equation, which describes damped oscillations [69][70][71][72].…”

Section: Example Of Problems With Chain Rule: Kaldor-type Model Of Bumentioning

confidence: 99%

“…Let us derive the equation of the Kaldor model of business cycles by using approach proposed by Chang and Smyth [68] (see also [70][71][72]). In the Kaldor model, instead of the standard accelerator equation I(t) = vY (1) (t) the dependence of investments on the rate of change of national income is considered in the form:…”

Section: Standard Kaldor-type Model Of Business Cyclesmentioning

confidence: 99%

Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models

Tarasov

2019

Mathematics

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This article is a review of problems and difficulties arising in the construction of fractional-dynamic analogs of standard models by using fractional calculus. These fractional generalizations allow us to take into account the effects of memory and non-locality, distributed lag, and scaling. We formulate rules (principles) for constructing fractional generalizations of standard models, which were described by differential equations of integer order. Important requirements to building fractional generalization of dynamical models (the rules for “fractional-dynamic generalizers”) are represented as the derivability principle, the multiplicity principle, the solvability and correspondence principles, and the interpretability principle. The characteristic properties of fractional derivatives of non-integer order are the violation of standard rules and properties that are fulfilled for derivatives of integer order. These non-standard mathematical properties allow us to describe non-standard processes and phenomena associated with non-locality and memory. However, these non-standard properties lead to restrictions in the sequential and self-consistent construction of fractional generalizations of standard models. In this article, we give examples of problems arising due to the non-standard properties of fractional derivatives in construction of fractional generalizations of standard dynamic models in economics.

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“…Ya hemos dicho que originalmente el modelo pretendía describir la dinámica atmosférica y que Haken extendió su aplicación al caso de cierto tipo de láseres; sin embargo, hay más: diversos modelos de sistemas mecánicos [12][13][14][15], hidrodinámicos [16][17][18] o incluso económicos [19][20][21] son isomorfos a las ecuaciones de Lorenz. También son numerosas las observaciones experimentales, como las de Weiss en láseres [22,23] u otras como las de Illing en norias de agua [24].…”

Section: C Versatilidad Del Modelo De Lorenzunclassified

Didactic application of numerical analysis in nonlinear dynamics: Lorenz model study

García-Ferrer¹,

Roldán²,

Silva³

et al. 2017

Opt. Pura Apl.

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ABSTRACT:We describe a practice designed for the numerical study of the Lorenz model that is a central model in the physics of lasers. The didactical objectives pursued in this practice have a dual nature, considering both the introduction to the knowledge of a physical paradigm of deterministic chaos as the training for the use of certain computational tools for its characterization. The method used to achieve programming is finding solutions of the Lorenz model and systematically studying of their temporal evolution using a Mathematica program. In the academic context, the practice is designed to be included in the curriculum of the degree in physics and to facilitate adaptation to other matters in this area, such as quantum optics, fluids, mechanical vibrations, etc. We first study the steady states, and their linear stability, of the Lorenz model equations and then numerically study the different types of dynamic behavior. We pay special attention to the deterministic chaotic behavior and to the sequence of bifurcations leading from periodic to chaotic behavior (routes to chaos).Key words: Lorenz model, chaos, nonlinear dynamics, laser, didactic, Mathematica. RESUMEN:Describimos una práctica diseñada para el estudio numérico de un modelo central en la física del láser, el modelo de Lorenz. Los objetivos didácticos que se persiguen en la práctica tienen una naturaleza doble, por un parte, la introducción al conocimiento de un paradigma físico del caos determinista y, por otra, la capacitación para la utilización de ciertas herramientas computacionales que permiten su caracterización. El método utilizado para alcanzarlos es la búsqueda de las soluciones del modelo de Lorenz y el estudio sistemático de su evolución temporal mediante el programa Mathematica. En el contexto académico, la práctica está diseñada para ser incluida en el currículum del grado en Física y para facilitar su adaptación a otras materias dentro de este ámbito, como puede ser óptica cuántica, fluidos, oscilaciones mecánicas, etc. Partiendo de las ecuaciones del modelo de Lorenz, estudiamos sus estados estacionarios y su estabilidad lineal, para después estudiar numéricamente los distintos tipos de comportamiento dinámico. Prestamos especial atención al comportamiento caótico determinista y a la secuencia de bifurcaciones que lleva de los comportamientos periódicos a los caóticos (rutas al caos).Palabras clave: Modelo de Lorenz, caos, dinámica no lineal, láser, didáctica, Mathematica. REFERENCES AND LINKS / REFERENCIAS Y ENLACES[1] E.N. Lorenz, "Deterministic nonperiodic flow", J. Atm. Sci. 20, 130-141 (1963).

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Business Cycle Theory

Cited by 48 publications

References 0 publications

The Labor Market and Business Cycle Theories

The Labor Market and Business Cycle Theories

Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models

Didactic application of numerical analysis in nonlinear dynamics: Lorenz model study

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