Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
A Stochastic Galerkin Method for the Fokker–Planck–Landau Equation with Random Uncertainties Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Stability Criteria for Some System of Delay Differential Equations

Authors : Yuya Kiri, Yoshihiro Ueda

Published in: Theory, Numerics and Applications of Hyperbolic Problems II

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, we study a system of linear differential equations with interaction effects of delay and derive some necessary and sufficient conditions concerned with the absolutely stable. We had already known many results about the scalar equations. On the other hand, the results of the delay systems are not many because the corresponding characteristic equation is too complicated. Under this situation, we introduce the simple and useful method to get the stability criteria and apply to some general system of delay differential equations.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Water Hammer Modeling for Water Networks via Hyperbolic PDEs and Switched DAEs
next chapter Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics
Literature
1.
P. Baldi, A. Atiya, How delays affect neural dynamics and learning. IEEE Trans. Neural Netw. 5, 612–621 (1994)CrossRef
2.
R. Bellman, K.L. Cooke, Differential-Difference Equations (Academic Press, New York, 1963)CrossRef
3.
S.A. Campbell, Stability and bifurcation of a simple neural network with multiple time delays. Fields Inst. Commun. 21, 65–79 (1999)MathSciNetMATH
4.
L.E. El’sgol’ts, S.B. Norkin, Introduction to the Theory and Application of Differential Equations with Deviating Arguments. Mathematics in Science and Engineering, vol. 105 (Academic Press, New York, 1973)
5.
6.
J.K. Hale, Theory of Functional Differential Equations. Applied Mathematics Sciences, vol. 3 (Springer, New York, 1977)CrossRef
7.
N.D. Hayes, Roots of the transcendental equation associated with a certain difference-differential equation. J. Lond. Math. Soc. 25, 226–232 (1950)MathSciNetCrossRef
8.
J.K. Hale, S.M.V. Lunel, Introduction to Functional Differential Equations. Applied Mathematical Sciences, vol. 99 (Springer, New York, 1993)CrossRef
9.
L.H. Lu, Numerical stability of the \({\theta }\)-methods for systems of differential equations with several delay terms. J. Comput. Appl. Math. 34(3), 291–304 (1991)
10.
Z. Lu, W. Wang, Global stability for two-species Lotka-Volterra systems with delay. J. Math. Anal. Appl. 208(1), 277–280 (1997)MathSciNetCrossRef
11.
G. Orosz, G. Stépán, Subcritical Hopf bifurcations in a car-following model with reaction-time delay. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462(2073), 2643–2670 (2006)MathSciNetCrossRef
12.
G. Orosz, R.E. Wilson, G. Stépán, Traffic jams: dynamics and control. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 368(1928), 4455–4479 (2010)MathSciNetCrossRef
13.
G. Peralta, Y. Ueda, Stability condition for a system of delay-differential equations and its application
14.
S. Ruan, Absolute stability, conditional stability and bifurcation in Kolmogorov-type predator-pray systems with discrete delays. Q. Appl. Math. 59(1), 159–173 (2001)MathSciNetCrossRef
15.
G. Stépán, Retarded Dynamical Systems: Stability and Characteristic Functions. Pitman Research Notes in Mathematics Series, vol. 210 (Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1989)
16.
M. Suzuki, H. Mastunaga, Stability criteria for a class of linear differential equations with off-diagonal delays. Discret. Contin. Dyn. Syst. 24(4), 1381–1391 (2009)MathSciNetCrossRef
17.
X.P. Yan, Y.D. Chu, Stability and bifurcation analysis for a delayed Lotka–Volterra predator-prey system. J. Comput. Appl. Math. 196(1), 198–210 (2006)MathSciNetCrossRef
Metadata
Title
Stability Criteria for Some System of Delay Differential Equations
Authors
Yuya Kiri
Yoshihiro Ueda
Copyright Year
2018
Book
Theory, Numerics and Applications of Hyperbolic Problems II

Print ISBN: 978-3-319-91547-0

Electronic ISBN: 978-3-319-91548-7

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91548-7_10

Premium Partners

    Image Credits