We continue the investigation of a one-dimensional piecewise linear map with two discontinuity points. Such a map may arise from a simple asset-pricing model with heterogeneous speculators, which can help us to explain the intricate bull and bear behavior of financial markets. Our focus is on bifurcation structures observed in the chaotic domain of the map's parameter space, which is associated with robust multiband chaotic attractors. Such structures, related to the map with two discontinuities, have been not studied before. We show that besides the standard bandcount adding and bandcount incrementing bifurcation structures, associated with two partitions, there exist peculiar bandcount adding and bandcount incrementing structures involving all three partitions. Moreover, the map's three partitions may generate intriguing bistability phenomena.
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A financial market model with two discontinuities: Bifurcation structures in the chaotic domain
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Research Article|
May 22 2018
A financial market model with two discontinuities: Bifurcation structures in the chaotic domain
Special Collection:
Nonlinear Economic Dynamics
Anastasiia Panchuk;
Anastasiia Panchuk
a)
1
Institute of Mathematics NASU
, 3 Tereshchenkivska Str., 01601 Kyiv, Ukraine
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Iryna Sushko
;
Iryna Sushko
b)
1
Institute of Mathematics NASU
, 3 Tereshchenkivska Str., 01601 Kyiv, Ukraine
2
Kyiv School of Economics
, 92-94 Dmytrivska Str., 01135 Kyiv, Ukraine
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Frank Westerhoff
Frank Westerhoff
c)
3
Department of Economics, University of Bamberg
, Feldkirchenstrasse 21, 96045 Bamberg, Germany
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a)
Electronic mail: nastyap@imath.kiev.ua
b)
Electronic mail: sushko@imath.kiev.ua
c)
Electronic mail: frank.westerhoff@uni-bamberg.de
Chaos 28, 055908 (2018)
Article history
Received:
January 31 2018
Accepted:
April 03 2018
Citation
Anastasiia Panchuk, Iryna Sushko, Frank Westerhoff; A financial market model with two discontinuities: Bifurcation structures in the chaotic domain. Chaos 1 May 2018; 28 (5): 055908. https://doi.org/10.1063/1.5024382
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