A 2D piecewise-linear discontinuous map arising in stock market modeling: Two overlapping period-adding bifurcation structures

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F23%3A10253042" target="_blank" >RIV/61989100:27510/23:10253042 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0960077923010445?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0960077923010445?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.chaos.2023.114143" target="_blank" >10.1016/j.chaos.2023.114143</a>

Result language

angličtina

Original language name

A 2D piecewise-linear discontinuous map arising in stock market modeling: Two overlapping period-adding bifurcation structures

Original language description

We consider a 2D piecewise-linear discontinuous map defined on three partitions that drives the dynamics of a stock market model. This model is a modification of our previous model associated with a map defined on two partitions. In the present paper, we add more realistic assumptions with respect to the behavior of sentiment traders. Sentiment traders optimistically buy (pessimistically sell) a certain amount of stocks when the stock market is sufficiently rising (falling); otherwise they are inactive. As a result, the action of the price adjustment is represented by a map defined by three different functions, on three different partitions. This leads, in particular, to families of attracting cycles which are new with respect to those associated with a map defined on two partitions. We illustrate how to detect analytically the periodicity regions of these cycles considering the simplest cases of rotation number 1/n, nGREATER-THAN OR EQUAL TO3, and obtaining in explicit form the bifurcation boundaries of the corresponding regions. We show that in the parameter space, these regions form two different overlapping period-adding structures that issue from the center bifurcation line. In particular, each point of this line, associated with a rational rotation number, is an issue point for two different periodicity regions related to attracting cycles with the same rotation number but with different symbolic sequences. Since these regions overlap with each other and with the domain of a locally stable fixed point, a characteristic feature of the map is multistability, which we describe by considering the corresponding basins of attraction. Our results contribute to the development of the bifurcation theory for discontinuous maps, as well as to the understanding of the excessively volatile boom-bust nature of stock markets. (C) 2023 The Author(s)

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

50200 - Economics and Business

Project

<a href="/en/project/GA23-06282S" target="_blank" >GA23-06282S: Evolutionary economic dynamics with finite populations: Modeling and applications</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Chaos, Solitons &amp; Fractals

ISSN

0960-0779

e-ISSN

1873-2887

Volume of the periodical

176

Issue of the periodical within the volume

November

Country of publishing house

GB - UNITED KINGDOM

Number of pages

14

Pages from-to

114143

UT code for WoS article

001097669600001

EID of the result in the Scopus database

2-s2.0-85173619620