Analytical expressions of periodic disequilibrium fluctuations generated by Hopf bifurcations in economic dynamics

Asada, Toichiro; Kalantonis, V. S.; Markakis, M. P.; Markellos, Panagiotis

doi:10.1016/j.amc.2011.12.063

Cited by 8 publications

(8 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In line with this development, open economy extensions of Kaldor´s (1940) non-linear business cycle model appeared in the publications by several authors. Asada (1995), , Asada, Inaba and Misawa (2001), Medveďová (2011) and Asada, Kalantonis, Markellos and Markellos (2012) extended the Kaldorian business cycle theory to the models of a small open economy under fixed and flexible exchange rates. Further progress in research in particular on questions concerning business cycles was made utilizing new knowledge on limit cycles which can be found, for example in the books by Bibikov (1979), Wiggins (1990), and Kuznetsov (2004).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a twocountry Kaldorian model of business cycles with fixed exchange rates: the case of Slovakia and the Czech Republic

Cisková¹,

Zimková²,

Zimka³

2020

Śląski Przegląd Statystyczny

View full text Add to dashboard Cite

In this paper, Asada´s five-dimensional nonlinear model describing the dynamic interaction of two regions connected through interregional trade and interregional capital movement with fixed exchange rates is applied to the conditions of Slovakia and the Czech Republic. The functions of consumptions, investments, interest rates, taxes, and net exports involved in the model are constructed based on quarterly data of these two countries from the period 2010-2017. The equilibrium was found and the conditions on the parameters were established, guaranteeing that the Jacobian matrix of the model has a pair of purely imaginary eigenvalues with the remaining three with negative real parts. The bifurcation equation of the model giving the information on the qualitative properties of its solutions around the equilibrium, including the existence of business cycles and their stability/instability, was obtained. Numerical simulations are presented showing that they are fully in compliance with the achieved theoretical results.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamics of a twocountry Kaldorian model of business cycles with fixed exchange rates: the case of Slovakia and the Czech Republic

Cisková¹,

Zimková²,

Zimka³

2020

Śląski Przegląd Statystyczny

View full text Add to dashboard Cite

show abstract

“…In the international literature, we encounter a large number of -dimensional nonlinear dynamical systems ( ≥ 3) in different areas of applied sciences, which are studied with respect to stability and local bifurcations generated by the variation of the involved parameters. We refer, for example, to recent relevant works in modern scientific disciplines like biosciences [1][2][3][4], energy systems [5,6], economics [7,8], and so forth. We also refer to classic dynamical systems like the Lorenz [9], Lü [10,11], and Chen [12] systems or to more general modified forms like [13].…”

Section: Introductionmentioning

confidence: 99%

On the Computation of Degenerate Hopf Bifurcations forn-Dimensional Multiparameter Vector Fields

Markakis

Douris

2016

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

The restriction of ann-dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration.

show abstract

“…Recently, many conflicting macroeconomic dynamic models have been generated. The classical model was proposed by Kaldor and the mathematical structure of the business cycle based on the Kaldorian concept has been researched extensively [9][10][11]. However, it must be noted that most of this research was based on closed economic systems with the exception of a few studies such as those of Lorenz, Asada, and a few others.…”

Section: Introductionmentioning

confidence: 99%

Stability and Hopf Bifurcation Analysis on a Nonlinear Business Cycle Model

Zhao

2016

Mathematical Problems in Engineering

View full text Add to dashboard Cite

This study begins with the establishment of a three-dimension business cycle model based on the condition of a fixed exchange rate. Using the established model, the reported study proceeds to describe and discuss the existence of the equilibrium and stability of the economic system near the equilibrium point as a function of the speed of market regulation and the degree of capital liquidity and a stable region is defined. In addition, the condition of Hopf bifurcation is discussed and the stability of a periodic solution, which is generated by the Hopf bifurcation and the direction of the Hopf bifurcation, is provided. Finally, a numerical simulation is provided to confirm the theoretical results. This study plays an important role in theoretical understanding of business cycle models and it is crucial for decision makers in formulating macroeconomic policies as detailed in the conclusions of this report.

show abstract

Analytical expressions of periodic disequilibrium fluctuations generated by Hopf bifurcations in economic dynamics

Cited by 8 publications

References 7 publications

Dynamics of a twocountry Kaldorian model of business cycles with fixed exchange rates: the case of Slovakia and the Czech Republic

Dynamics of a twocountry Kaldorian model of business cycles with fixed exchange rates: the case of Slovakia and the Czech Republic

On the Computation of Degenerate Hopf Bifurcations forn-Dimensional Multiparameter Vector Fields

Stability and Hopf Bifurcation Analysis on a Nonlinear Business Cycle Model

Contact Info

Product

Resources

About