Stability criteria for certain second order delay differential equations

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Volumn 10, Issue 4, 2003, Pages 593-621

  Cahlon, Baruch ^a   Schmidt, Darrell ^a  

^a OAKLAND UNIVERSITY   (United States)

Author keywords

Asymptotic stability; Characteristic functions; Delay; Stability criteria; Stability regions; Sufficient conditions

Indexed keywords

EID: 3042518378     PISSN: 12013390     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. I. Arieh, and T. Josef, Stability and asymptotic stability of func-tional-differential equations J. London Math. Soc. 51 (1995), 559-572.
2. R. Bellman and K. L. Cooke, Differential-difference equations (1963), Academic Press, New York.
3. S. J. Bhatt and C. S. Hsu, Stability criteria for second order dynamical systems with time lag, Journal of Applied Mechanics 33 (1966), 113-118.
4. F. G. Boese, Stability criteria for second-order dynamical systems involving several time delays, SIAM J. Math. Anal. 26 (1995), 1306-1330.
5. Bugong Xu, Stability criteria for linear time-invariant systems with mutiple delays, Journal of Mathematical Analysis and Application 252 (2000), 484-494.
6. B. Cahlon, and D. Schmidt, On stability of systems of delay differential equations, Journal of Compt. and Appl. Math 10 (1999), 137-158.
7. S. A. Campbell, J. Belair, T. Ohira, and J. Milton, Limit cycles, Tori, and Complex Dynamics in a second-order differential equation with delayed negative feedback, J. of Dynamics and Differential Equations 7 (1995), 213-236.
8. K. L. Cooke and Z. Grossman, Stability and oscillation in delay differential equations of population dynamics, Kluwer Academic Publishers.
9. K. Gopalsamy, Discrete delay, distributed delay and stability switches, Journal of Mathematical Analysis and Applications 86 (1982), 592-627.
10. J. K. Hale, Theory of functional differential equations, Springer Verlag, New York, (1977).
11. T. Hara, M. Rinko and T. Morii, Asymptotic stability condition for linear differential-difference equations with delays, Dynamic Systems Appl. 6 (1997), 493-506.
12. T. Hara, and J. Sugie, Stability region for systems of differential-difference equations, Funk Ekvac. 39 (1996), 505-515.
13. G. D. Hu, and T. Mitsu, Stability of numerical methods for systems of neutral delay differential equations, BIT 35 (1995), 69-86.
14. Huang, Wenzhang and Huang, Wen Zhang, On asymptotic stability for linear delay equations, Differential and Integral 4 (1991), 1303-1310.
15. J. Karsai, On the asymptotic behavior of the solutions of a second order differential equation with small damping, Acta Mathematica Hungarica 34 (1999), 1721-1723.
16. V. B. Kolmanovskii, Stability of some test equations with delay, SIAM J. Math. Anal. 25 (1994), 948-961.
17. Y. Kuang, Delay differential equations with applications in population dynamic, Academic Press, San Diego, CA (1993).
18. N. MacDonald, Biological delay systems: linear stability theory, Cambridge University Press, Cambridge-New York (1989).
19. P. Manuel, Asymptotic solutions for second order delay differential equations, Nonlinear Analysis 28 (1997), 1729-1740.
20. L. S. Pontryagin, On zeros of some transcendental functions, Akad Nouk SSSR, Ser. Mat. 6 (1942), 115-134. The English translation is given in Amer. Math. Soc. Transl., Ser. 2, Vol. 1, 1955, pp. 95-110.
21. L. S. Pontryagin, On zeros of some transcendental functions, Akad Nouk SSSR, Ser. Mat. 6 (1942), 115-134. The English translation is given in Amer. Math. Soc. Transl., Ser. 2, Vol. 1, 1955, pp. 95-110.
22. V. A. Shcheglov, Stability of solutions of a second order equation with delay, Differential equation (journal translation) 34 (1999), 1721-1723.
23. C. R. Steel, Studies of the ear, 17 (1979), Lectures in Applied Mathematics, 69-71.
24. G. Stépán, Retarded dynamical systems: stability and characteristic functions, (Research Notes in Math.) Series, 210, John Wiley and Sons.
25. S. A. Tobias, Machine tool vibrations, (1965) Blackie, London.
26. L. Xiaoxin, and W. XiaoJun, Stability for differential difference equations, J. Math. Anal. Appl. 174 (1991), 84-102.
27. Yu Yuanhong Stability criteria for linear second order delay differential systems, Acta Mathematica Applicata Sinica 4 (1988), 109-112.