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2018 | OriginalPaper | Buchkapitel

Stability Criteria for Some System of Delay Differential Equations

verfasst von : Yuya Kiri, Yoshihiro Ueda

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

Verlag: Springer International Publishing

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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.

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Literatur
1.
Zurück zum Zitat P. Baldi, A. Atiya, How delays affect neural dynamics and learning. IEEE Trans. Neural Netw. 5, 612–621 (1994)CrossRef P. Baldi, A. Atiya, How delays affect neural dynamics and learning. IEEE Trans. Neural Netw. 5, 612–621 (1994)CrossRef
2.
Zurück zum Zitat R. Bellman, K.L. Cooke, Differential-Difference Equations (Academic Press, New York, 1963)CrossRef R. Bellman, K.L. Cooke, Differential-Difference Equations (Academic Press, New York, 1963)CrossRef
3.
Zurück zum Zitat S.A. Campbell, Stability and bifurcation of a simple neural network with multiple time delays. Fields Inst. Commun. 21, 65–79 (1999)MathSciNetMATH S.A. Campbell, Stability and bifurcation of a simple neural network with multiple time delays. Fields Inst. Commun. 21, 65–79 (1999)MathSciNetMATH
4.
Zurück zum Zitat 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) 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.
Zurück zum Zitat J.K. Hale, Theory of Functional Differential Equations. Applied Mathematics Sciences, vol. 3 (Springer, New York, 1977)CrossRef J.K. Hale, Theory of Functional Differential Equations. Applied Mathematics Sciences, vol. 3 (Springer, New York, 1977)CrossRef
7.
Zurück zum Zitat N.D. Hayes, Roots of the transcendental equation associated with a certain difference-differential equation. J. Lond. Math. Soc. 25, 226–232 (1950)MathSciNetCrossRef 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.
Zurück zum Zitat J.K. Hale, S.M.V. Lunel, Introduction to Functional Differential Equations. Applied Mathematical Sciences, vol. 99 (Springer, New York, 1993)CrossRef J.K. Hale, S.M.V. Lunel, Introduction to Functional Differential Equations. Applied Mathematical Sciences, vol. 99 (Springer, New York, 1993)CrossRef
9.
Zurück zum Zitat 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) 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.
Zurück zum Zitat Z. Lu, W. Wang, Global stability for two-species Lotka-Volterra systems with delay. J. Math. Anal. Appl. 208(1), 277–280 (1997)MathSciNetCrossRef 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.
Zurück zum Zitat 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 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.
Zurück zum Zitat 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 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.
Zurück zum Zitat G. Peralta, Y. Ueda, Stability condition for a system of delay-differential equations and its application G. Peralta, Y. Ueda, Stability condition for a system of delay-differential equations and its application
14.
Zurück zum Zitat 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 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.
Zurück zum Zitat 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) 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.
Zurück zum Zitat 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 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.
Zurück zum Zitat 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 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
Metadaten
Titel
Stability Criteria for Some System of Delay Differential Equations
verfasst von
Yuya Kiri
Yoshihiro Ueda
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-91548-7_10

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