Randomized Sharkovsky-type theorems and their application to random impulsive differential equations and inclusions on tori
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Randomized Sharkovsky-type theorems and their application to random impulsive differential equations and inclusions on tori
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Stochastics and Dynamics
ISSN
0219-4937
e-ISSN
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Volume of the periodical
19
Issue of the periodical within the volume
5
Country of publishing house
SG - SINGAPORE
Number of pages
30
Pages from-to
"1950036-1"-"1950036-30"
UT code for WoS article
000481992200004
EID of the result in the Scopus database
2-s2.0-85060024323