Abundance of Weird Quasiperiodic Attractors in Piecewise Linear Discontinuous Maps

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F25%3A10258590" target="_blank" >RIV/61989100:27510/25:10258590 - isvavai.cz</a>

Result on the web

<a href="https://www.worldscientific.com/doi/10.1142/S0218127425300307" target="_blank" >https://www.worldscientific.com/doi/10.1142/S0218127425300307</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218127425300307" target="_blank" >10.1142/S0218127425300307</a>

Result language

angličtina

Original language name

Abundance of Weird Quasiperiodic Attractors in Piecewise Linear Discontinuous Maps

Original language description

In this work, we consider a class of n-dimensional, n &gt;= 2, piecewise linear discontinuous maps that can exhibit a new type of attractor, called a weird quasiperiodic attractor. While the dynamics associated with these attractors may appear chaotic, we prove that chaotic attractors cannot occur. The considered class of n-dimensional maps allows for any finite number of partitions, separated by various types of discontinuity sets. The key characteristic, beyond discontinuity, is that all functions defining the map have the same real fixed point. These maps cannot have hyperbolic cycles other than the fixed point itself. We consider the two-dimensional case in detail. We prove that in nongeneric cases, the restriction, or the first return, of the map to a segment of straight line issuing from the fixed point is reducible to a piecewise linear circle map. The generic attractor, different from the fixed point, is a weird quasiperiodic attractor, which may coexist with other attractors or attracting sets. We illustrate the existence of these attractors through numerous examples, using functions with different types of Jacobian matrices, as well as with different types of discontinuity sets. An application to a financial market modeling shows the role of regulator that maps in our class can have, leading to endogenous nonregular dynamics. In some cases, we describe possible mechanisms leading to the appearance of these attractors. We also give examples in the three-dimensional space. Several properties of this new type of attractor remain open for further investigation.

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

10100 - Mathematics

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

Name of the periodical

International Journal of Bifurcation and Chaos

ISSN

0218-1274

e-ISSN

1793-6551

Volume of the periodical

35

Issue of the periodical within the volume

15

Country of publishing house

SG - SINGAPORE

Number of pages

30

Pages from-to

2530030

UT code for WoS article

001574352000001

EID of the result in the Scopus database

2-s2.0-105016468018