Randomized Sharkovsky-type theorems and their application to random impulsive differential equations and inclusions on tori

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F19%3A73594947" target="_blank" >RIV/61989592:15310/19:73594947 - isvavai.cz</a>

Výsledek na webu

<a href="https://obd.upol.cz/id_publ/333174833" target="_blank" >https://obd.upol.cz/id_publ/333174833</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0219493719500369" target="_blank" >10.1142/S0219493719500369</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Randomized Sharkovsky-type theorems and their application to random impulsive differential equations and inclusions on tori

Popis výsledku v původním jazyce

Our randomized versions of the Sharkovsky-type cycle coexistence theorems on tori and, in particular, on the circle are applied to random impulsive differential equations and inclusions. The obtained effective coexistence criteria for random subharmonics with various periods are formulated in terms of the Lefschetz numbers (in dimension one, in terms of degrees) of the impulsive maps and their iterates w.r.t. the (deterministic) state variables. Otherwise, the forcing properties of certain periods of the given random subharmonics are employed, provided there exists a random harmonic solution. In the single-valued case, the exhibition of deterministic chaos in the sense of Devaney is detected for random impulsive differential equations on the factor space R/Z. Several simple illustrative examples are supplied.

Název v anglickém jazyce

Randomized Sharkovsky-type theorems and their application to random impulsive differential equations and inclusions on tori

Popis výsledku anglicky

Our randomized versions of the Sharkovsky-type cycle coexistence theorems on tori and, in particular, on the circle are applied to random impulsive differential equations and inclusions. The obtained effective coexistence criteria for random subharmonics with various periods are formulated in terms of the Lefschetz numbers (in dimension one, in terms of degrees) of the impulsive maps and their iterates w.r.t. the (deterministic) state variables. Otherwise, the forcing properties of certain periods of the given random subharmonics are employed, provided there exists a random harmonic solution. In the single-valued case, the exhibition of deterministic chaos in the sense of Devaney is detected for random impulsive differential equations on the factor space R/Z. Several simple illustrative examples are supplied.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Stochastics and Dynamics

ISSN

0219-4937

e-ISSN

—

Svazek periodika

19

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

30

Strana od-do

"1950036-1"-"1950036-30"

Kód UT WoS článku

000481992200004

EID výsledku v databázi Scopus

2-s2.0-85060024323