Existence of chaos in the plane $mathbb{R}^2$ and its application in macroeconomics
Result description
The Devaney, Li-Yorke and distributional chaos in the plane R-2 can occur in the continuous dynamical system generated by Euler equation branching. Euler equation branching is a type of differential inclusion (x) over dot is an element of{f(x), g(x)}, where f,g : X subset of R-n -> R-n are continuous and f (x) not equal g(x) in every point x is an element of X. Stockman and Raines (2010) defined the so-called chaotic set in the plane R-2 whose existence leads to the existence of Devaney, Li-Yorke and distributional chaos. In this paper, we follow up on Stockman and Raines (2010) and we show that chaos in the plane R-2 is always admitted for hyperbolic singular points in both branches not lying in the same point in R-2. But the chaos existence is also caused by a set of solutions of Euler equation branching. We research this set of solutions. In the second part we create the new overall macroeconomic equilibrium model called IS-LM/QY-ML model. This model is based on the fundamental macr
Keywords
Euler equation branchingchaosIS-LM/QY-ML modeleconomic cycle
The result's identifiers
Result code in IS VaVaI
Result on the web
http://www.sciencedirect.com/science/article/pii/S0096300315001277
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Existence of chaos in the plane $mathbb{R}^2$ and its application in macroeconomics
Original language description
The Devaney, Li-Yorke and distributional chaos in the plane R-2 can occur in the continuous dynamical system generated by Euler equation branching. Euler equation branching is a type of differential inclusion (x) over dot is an element of{f(x), g(x)}, where f,g : X subset of R-n -> R-n are continuous and f (x) not equal g(x) in every point x is an element of X. Stockman and Raines (2010) defined the so-called chaotic set in the plane R-2 whose existence leads to the existence of Devaney, Li-Yorke and distributional chaos. In this paper, we follow up on Stockman and Raines (2010) and we show that chaos in the plane R-2 is always admitted for hyperbolic singular points in both branches not lying in the same point in R-2. But the chaos existence is also caused by a set of solutions of Euler equation branching. We research this set of solutions. In the second part we create the new overall macroeconomic equilibrium model called IS-LM/QY-ML model. This model is based on the fundamental macr
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Applied Mathematics and Computation
ISSN
0096-3003
e-ISSN
—
Volume of the periodical
258
Issue of the periodical within the volume
1 May 2015
Country of publishing house
US - UNITED STATES
Number of pages
30
Pages from-to
237-266
UT code for WoS article
000351668500026
EID of the result in the Scopus database
2-s2.0-84923632703
Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2015