Detail publikačního výsledku

Delay-dependent stability switches in fractional differential equations

KISELA, T.; ČERMÁK, J.

Originální název

Delay-dependent stability switches in fractional differential equations

Anglický název

Delay-dependent stability switches in fractional differential equations

Druh

Článek WoS

Originální abstrakt

This paper discusses stability properties of a linear fractional delay differential system involving both delayed as well as non-delayed terms. As a main result, the explicit stability dependence on a changing time delay is described, including conditions for the appearance, number and exact calculations of stability switches for this system when its stability property turns into instability and vice versa in view of a monotonically increasing lag. Some supporting asymptotic results are stated as well. The proof technique is based on analysis of the generalized delay exponential function of the Mittag-Leffler type combined with D-decomposition method. The obtained results are illustrated via a fractional Lotka-Volterra population model and applied to a stabilization problem of the control theory.

Anglický abstrakt

This paper discusses stability properties of a linear fractional delay differential system involving both delayed as well as non-delayed terms. As a main result, the explicit stability dependence on a changing time delay is described, including conditions for the appearance, number and exact calculations of stability switches for this system when its stability property turns into instability and vice versa in view of a monotonically increasing lag. Some supporting asymptotic results are stated as well. The proof technique is based on analysis of the generalized delay exponential function of the Mittag-Leffler type combined with D-decomposition method. The obtained results are illustrated via a fractional Lotka-Volterra population model and applied to a stabilization problem of the control theory.

Klíčová slova

Fractional delay differential equation; Stability switch; Asymptotic behaviour; Stabilization

Klíčová slova v angličtině

Fractional delay differential equation; Stability switch; Asymptotic behaviour; Stabilization

Autoři

KISELA, T.; ČERMÁK, J.

Rok RIV

2020

Vydáno

01.12.2019

Nakladatel

Elsevier

Místo

RADARWEG 29, 1043 NX AMSTERDAM, NETHERLANDS

ISSN

1007-5704

Periodikum

Communications in Nonlinear Science and Numerical Simulation

Svazek

79

Číslo

1

Stát

Nizozemsko

Strany od

1

Strany do

19

Strany počet

19

URL

https://www.sciencedirect.com/science/article/pii/S1007570419302102

BibTex

@article{BUT159358,
  author="Tomáš {Kisela} and Jan {Čermák}",
  title="Delay-dependent stability switches in fractional differential equations",
  journal="Communications in Nonlinear Science and Numerical Simulation",
  year="2019",
  volume="79",
  number="1",
  pages="1--19",
  doi="10.1016/j.cnsns.2019.104888",
  issn="1007-5704",
  url="https://www.sciencedirect.com/science/article/pii/S1007570419302102"
}