Stability Conditions of a Class of Linear Retarded Differential Systems

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Serbun Ufuk Deger, Yasar Bolat, Stability Conditions of a Class of Linear Retarded Differential Systems, Int. J. Anal. Appl., 16 (4) (2018), 454-461.

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Serbun Ufuk Deger, Yasar Bolat

Abstract

In this paper, we give some new necessary and sufficient conditions for the asymptotic stability of a linear retarded differential system with two delays
x”²(t)+(1-a)x(t)+A(x(t-k)+x(t-l))=0, t≥0,
where a<1 is a real number, A is a 2×2 real constant matrix, and k, l are positive numbers such that k>l.

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References

  1. H. Matsunaga, Delay Dependent and Delay Independent Stability Criteria For A Delay Differential System, American Mathematical Society, 136 Fields Inst. Commun. 42 (2008), 4305-4312.
  2. K. L. Cooke and P. van den Driessche, On zeroes of some transcendental equations, Funkcial.Ekvacioj, 29 (1986), 77-90.
  3. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993.
  4. K. L. Cooke and Z. Grossman, Discrete delay, distributed delay and stability switches, J. Math. Anal. Appl. 86 (1982), 592-627.
  5. S.Ruan and J.Wei, On The Zeros Of Transcendental Functions With Applications To Stability Of Delay Differential Equations With Two Delays, Dynamic of Continuous, Discr. impuls. Syst. (2003), 863-874.
  6. J.K.Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993.
  7. S. Elaydi, An Introduction to Difference Equations, 3rd ed., Springer-Verlag, New York, 2005.
  8. T. Khokhlovaa, M. Kipnis, V. Malygina, Discrete delay, The stability cone for a delay differential matrix equation, Appl. Math. Lett. 24 (2011), 742-745.
  9. J. Cermák, J.Jánsky, Stability switches in linear delay difference equations, Appl. Math. Comput. 243 (2014) 755-766.
  10. Jana Hrabalova, Stability Properties of a Discrrtized Neutral Delay Differential Equation, Tatra Mt. Math. Publ. 54 (2013), 83-92
  11. H. Nakajima, On the Stability of a linear Retarded Differential-Difference Equation, Funkcialaj Ekvacioj. 57 (2014), 43-56
  12. T. Hara, S. Sakata, An application of the Hurwitz theorem to the root analysis of the characteristic equation, Appl. Math. Lett. 24 (2011) 12-15
  13. H. Smith, An Introduction to Delay Differential Equations with Applications to The Life Science, Springer, New York 2010.
  14. H. I .Freedman, Y.Kuang, Stability switches in linear scalar neutral delay equation, Funkcial. Ekvac. 34 (1991), 187-209.
  15. R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York, 1963.