Complex economic dynamics: Chaotic saddle, crisis and intermittency

Chian, Abraham C.‐L.; Rempel, Erico L.; Rogers, Colin

doi:10.1016/j.chaos.2005.08.218

Cited by 104 publications

(71 citation statements)

References 66 publications

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“…Contrary to many business cycle studies (e.g., [6][7][8][9][10][11][12]), the absence of nonlinearity in our simpler setup rules out the possibility of limit cycles and other more complex economic behaviours (typically, a Hopf bifurcation requires the branching from an equilibrium into a periodic orbit. Here, we use the term "Hopf" just to highlight the fact that a fixed point looses stability as the eigenvalues of the Jacobian at the fixed point cross the imaginary axis of the complex plain).…”

Section: Introductionmentioning

confidence: 99%

Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab

Gaspar

2018

Journal of Applied Mathematics

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This paper aims to connect the bridge between analytical results and the use of the computer for numerical simulations in economics. We address the analytical properties of a simple dynamic aggregate demand and aggregate supply (AD-AS) model and solve it numerically. The model undergoes a bifurcation as its steady state smoothly interchanges stability depending on the relationship between the impact of real interest rate on demand for liquidity and how fast agents revise their expectations on inflation. Using code embedded into a unique function in Matlab, we plot the numerical solutions of the model and simulate different dynamic adjustments using different parameter values. The same function also accommodates the analysis of the impacts of fiscal and monetary policy and supply side shocks on the steady state and the transition dynamics of the model.

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Section: Introductionmentioning

confidence: 99%

Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab

Gaspar

2018

Journal of Applied Mathematics

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“…Además de lo anterior, el análisis de sincronización de fase constituye una herramienta nueva para describir la dinámica de un sistema tan complejo que en las últimas décadas ha recurrido al análisis de sistemas puramente fenomenológicos, ejemplos de estos últimos pueden ser vistos en Chian, Rempel y Rogers (2006) o Volos, Kyprianidis y Stouboulos (2012), los cuales constituyen una tecnología emergente en el análisis económico cuya principal virtud consiste en que sus resultados no dependen de los tradicionales supuestos econométricos como normalidad, no correlación entre los errores, ergodicidad, homocedasticidad, entre otros. Lo que la compara favorablemente respecto a las metodologías tradicionales de causalidad, como la de Granger (ejemplos de su uso son los trabajos de Thornton (1996) Jung y Marshall (1985) o Chow (1987) Una vez comparada la efectividad de esta metodología contra otras ya usadas en esta clase de estudios, se presentan los resultados de la investigación en la que se determina cuál de las series es la variable maestra de todo el sistema.…”

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Sincronización comercial e industrial en el TLCAN, un estudio de sincronización de fase

Villarreal

Ruiz

Aké³

2017

ETYP

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ResumenEn este trabajo se contrasta la hipótesis de que los ciclos de crecimiento individuales de los tres países que integran el área del Tratado de Libre Comercio de América del Norte (Tlcan) durante el periodo 1993-2015 han tendido a sincronizarse, para lo cual utilizamos la técnica de sincronización de fase. Ésta permite establecer la causalidad entre variables económicas sin necesidad de hacer los supuestos de esfericidad o ergodicidad tradicionales en el mode lado econométrico. Este trabajo aporta evidencia empírica para establecer que los ciclos eco nómicos individuales de Canadá, México y Estados Unidos están sincronizados con las fluctuaciones industriales de Estados Unidos, siendo éste el que encabeza los cambios en las fluctuaciones del área del Tlcan. Adicionalmente, se hacen mediciones sobre la duración de los enganches de sincronización de fase al interior de cada ciclo individual y en el conjunto de los tres ciclos al interior del Tlcan, así mismo se relacionan los periodos de enganche (y su pérdida) de los ciclos con el desempeño macroeconómico de las tres economías estudiadas. Palabras clave: Juglar, ciclo de negocios, integración económica. Clasificación jel: E11, E32, F15 abstRact In this paper, we contrast the hypothesis that individual growth cycles of the three countries that form the area of the North America Free Trade Agreement (nafTa) in the period 1993 -2015 have tended to be synchronized, for which we use the technique of phase synchronization. This allows us to establish causality between economic variables without making assumptions of sphericity or ergodicity, traditional on econometric modeling. This paper provides empirical evidence to confirm that individual business cycles in Canada, Mexico, and the United States are synchronized with industrial fluctuations in the United States, which act as triggers of change for fluctuations in the nafTa area. In addition, measurements of the duration of the linkage of the phase synchronization within each individual cycle and in all three cycles within nafTa are made, likewise hitch (and loss) periods are linked with the macroeconomic performance of the three economies studied.

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“…In recent years, study on chaos is one of the most interesting research topics in real and physical systems [1][2][3][4]. In 1985, chaotic behavior was discovered in financial systems [5].…”

Section: Introductionmentioning

confidence: 99%

Modified Function Projective Synchronization for a Partially Linear and Fractional-Order Financial Chaotic System with Uncertain Parameters

Yang

Cao

2017

Discrete Dynamics in Nature and Society

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This paper investigates the modified function projective synchronization between fractional-order chaotic systems, which are partially linear financial systems with uncertain parameters. Based on the stability theory of fractional-order systems and the Lyapunov matrix equation, a controller is obtained for the synchronization between fractional-order financial chaotic systems. Using the controller, the error systems converged to zero as time tends to infinity, and the uncertain parameters were also estimated so that the phenomenon of parameter distortion was effectively avoided. Numerical simulations demonstrate the validity and feasibility of the proposed method.

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Complex economic dynamics: Chaotic saddle, crisis and intermittency

Cited by 104 publications

References 66 publications

Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab

Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab

Sincronización comercial e industrial en el TLCAN, un estudio de sincronización de fase

Modified Function Projective Synchronization for a Partially Linear and Fractional-Order Financial Chaotic System with Uncertain Parameters

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