On the bifurcation of limit cycles in a dynamic model of a small open economy

Makovínyiová, Katarína; Zimka, Rudolf

doi:10.1017/s0956792513000053

Cited by 2 publications

References 6 publications

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On the birth and death of algebraic limit cycles in quadratic differential systems

Llibre¹,

Oliveira

Zhao³

2020

Eur. J. Appl. Math

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In 1958 started the study of the families of algebraic limit cycles in the class of planar quadratic polynomial differential systems. In the present we known one family of algebraic limit cycles of degree 2 and four families of algebraic limit cycles of degree 4, and that there are no limit cycles of degree 3. All the families of algebraic limit cycles of degree 2 and 4 are known, this is not the case for the families of degree higher than 4. We also know that there exist two families of algebraic limit cycles of degree 5 and one family of degree 6, but we do not know if these families are all the families of degree 5 and 6. Until today it is an open problem to know if there are algebraic limit cycles of degree higher than 6 inside the class of quadratic polynomial differential systems. Here we investigate the birth and death of all the known families of algebraic limit cycles of quadratic polynomial differential systems.

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On the birth and death of algebraic limit cycles in quadratic differential systems

Llibre¹,

Oliveira

Zhao³

2020

Eur. J. Appl. Math

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On dynamics in a four-dimensional model of a small open economy

Grausová¹,

Hužvár²,

Zimka³

2019

Proceedings of the 22nd International Scientific Conference on Applications of Mathematics and Statistics in Economics (AMSE 20

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In the paper, a four-dimensional nonlinear macroeconomic model of a small open economy describing the development of net real national income, real physical capital stock, nominal interest rate and nominal money stock is analysed. The functions of investment, savings, real income tax, liquidity preference and net exports that are included in the model are set up in accordance with economic theories. Therefore, the dependence of investments on net real national income is captured through an S-shaped curve, and the dependence of investments on nominal interest rate is modelled by an inverse of S-shaped curve. The Hopf bifurcation is applied to determine the bifurcation parameter of the model, to formulate the bifurcation equation, and to make a statement on the existence of business cycles.

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On the bifurcation of limit cycles in a dynamic model of a small open economy

Cited by 2 publications

References 6 publications

On the birth and death of algebraic limit cycles in quadratic differential systems

On the birth and death of algebraic limit cycles in quadratic differential systems

On dynamics in a four-dimensional model of a small open economy

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