Abundance of Weird Quasiperiodic Attractors in Piecewise Linear Discontinuous Maps

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Abundance of Weird Quasiperiodic Attractors in Piecewise Linear Discontinuous Maps

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Abundance of Weird Quasiperiodic Attractors in Piecewise Linear Discontinuous Maps

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/GA22-28882S" target="_blank" >GA22-28882S: Interakce mezi finančními trhy a reálným sektorem: Modelování, experimenty a politika</a><br>

Návaznosti

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

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

International Journal of Bifurcation and Chaos

ISSN

0218-1274

e-ISSN

1793-6551

Svazek periodika

35

Číslo periodika v rámci svazku

15

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

30

Strana od-do

2530030

Kód UT WoS článku

001574352000001

EID výsledku v databázi Scopus

2-s2.0-105016468018