Dynamics of 1D discontinuous maps with multiple partitions and linear functions having the same fixed point. An application to financial market modeling

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F25%3A10258592" target="_blank" >RIV/61989100:27510/25:10258592 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0167278925003720" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0167278925003720</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.physd.2025.134895" target="_blank" >10.1016/j.physd.2025.134895</a>

Result language
angličtina
Original language name
Dynamics of 1D discontinuous maps with multiple partitions and linear functions having the same fixed point. An application to financial market modeling
Original language description
Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a finite number of partitions and functions sharing the same real fixed point. We show that the dynamics of this class of maps can be analyzed using the well-known piecewise linear circle map. We prove that their bounded behavior, when unrelated to the fixed point, may consist of either nonhyperbolic cycles or quasiperiodic orbits densely filling certain segments, with possible coexistence. A corresponding model describing the price dynamics of a financial market serves as an illustrative example. While simulated model dynamics may be mistaken for chaotic behavior, our results demonstrate that they are quasiperiodic.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10300 - Physical sciences

Project
<a href="/en/project/GA22-28882S" target="_blank" >GA22-28882S: Interaction between Financial Markets and Real Sector: Modeling, Experiments, and Policy</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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