A cyclic system with delay and its characteristic equation

J 2020

A cyclic system with delay and its characteristic equation

HASÍK, Karel, Sergei TROFIMCHUK, Anatoli F. IVANOV and Elena BRAVERMAN

Basic information

Original name

A cyclic system with delay and its characteristic equation

Authors

HASÍK, Karel (203 Czech Republic, belonging to the institution), Sergei TROFIMCHUK (804 Ukraine, guarantor), Anatoli F. IVANOV (804 Ukraine) and Elena BRAVERMAN (124 Canada)

Edition

Discrete and Continuous Dynamical Systems - Series S, Springfield, American Institute of Mathematical Sciences, 2020, 1937-1632

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Discrete and Continuous Dynamical Systems - Series S

RIV identification code

RIV/47813059:19610/20:A0000074

Organization unit

Mathematical Institute in Opava

DOI

http://dx.doi.org/10.3934/dcdss.2020001

UT WoS

000496422500002

Keywords in English

Cyclic delay systems; sign feedback; overall negative feedback; linearization; characteristic equation; leading eigenvalue; eigenvalues with positive real parts; asymptotic behavior of eigenvalues; monotone solutions; oscillating solutions

Abstract

V originále

A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the existence of monotone solutions are derived in terms of roots of the characteristic equation.

Citovat

HASÍK, Karel, Sergei TROFIMCHUK, Anatoli F. IVANOV and Elena BRAVERMAN. A cyclic system with delay and its characteristic equation. Discrete and Continuous Dynamical Systems - Series S. Springfield: American Institute of Mathematical Sciences, 2020, vol. 13, No 1, p. 1-29. ISSN 1937-1632. Available from: https://dx.doi.org/10.3934/dcdss.2020001.

@article{39683,
   author = {Hasík, Karel and Trofimchuk, Sergei and Ivanov, Anatoli F. and Braverman, Elena},
   article_location = {Springfield},
   article_number = {1},
   doi = {http://dx.doi.org/10.3934/dcdss.2020001},
   keywords = {Cyclic delay systems; sign feedback; overall negative feedback; linearization; characteristic equation; leading eigenvalue; eigenvalues with positive real parts; asymptotic behavior of eigenvalues; monotone solutions; oscillating solutions},
   language = {eng},
   issn = {1937-1632},
   journal = {Discrete and Continuous Dynamical Systems - Series S},
   title = {A cyclic system with delay and its characteristic equation},
   url = {http://www.aimsciences.org/article/doi/10.3934/dcdss.2020001},
   volume = {13},
   year = {2020}
}

TY  - JOUR
ID  - 39683
AU  - Hasík, Karel - Trofimchuk, Sergei - Ivanov, Anatoli F. - Braverman, Elena
PY  - 2020
TI  - A cyclic system with delay and its characteristic equation
JF  - Discrete and Continuous Dynamical Systems - Series S
VL  - 13
IS  - 1
SP  - 1-29
EP  - 1-29
PB  - American Institute of Mathematical Sciences
SN  - 19371632
KW  - Cyclic delay systems
KW  - sign feedback
KW  - overall negative feedback
KW  - linearization
KW  - characteristic equation
KW  - leading eigenvalue
KW  - eigenvalues with positive real parts
KW  - asymptotic behavior of eigenvalues
KW  - monotone solutions
KW  - oscillating solutions
UR  - http://www.aimsciences.org/article/doi/10.3934/dcdss.2020001
L2  - http://www.aimsciences.org/article/doi/10.3934/dcdss.2020001
N2  - A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the existence of monotone solutions are derived in terms of roots of the characteristic equation.
ER  -

HASÍK, Karel, Sergei TROFIMCHUK, Anatoli F. IVANOV and Elena BRAVERMAN. A cyclic system with delay and its characteristic equation. \textit{Discrete and Continuous Dynamical Systems - Series S}. Springfield: American Institute of Mathematical Sciences, 2020, vol.~13, No~1, p.~1-29. ISSN~1937-1632. Available from: https://dx.doi.org/10.3934/dcdss.2020001.

Detailed Information on Publication Record