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. |
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@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.
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