Stability analysis of linear fractional differential system with multiple time delays

Nonlinear Dynamics

Volumn 48, Issue 4, 2007, Pages 409-416

  Deng, Weihua ^a,b   Li, Changpin ^b   Lü, Jinhu ^c  

^a LANZHOU UNIVERSITY   (China)

^b SHANGHAI UNIVERSITY   (China)

^c CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Delay; Duffing oscillator; Linear fractional differential system; Stability; Synchronization

Indexed keywords

ASYMPTOTIC ANALYSIS; LYAPUNOV METHODS; MATRIX ALGEBRA; PARAMETER ESTIMATION; SYNCHRONIZATION; SYSTEM STABILITY;

DELAY; DUFFING OSCILLATORS; LINEAR FRACTIONAL DIFFERENTIAL SYSTEMS; SPATIAL DIMENSION; TIME DELAYS;

DIFFERENTIAL EQUATIONS;

EID: 33947133956     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-006-9094-0     Document Type: Article

References (22)

1. Hale, J.K., Verdugn Lunel, S.M., Introduction to Functional Differential Equations. Springer-Verlag, New York (1991)
2. Deng, W.H., Wu, Y.J., Li, C.P.: Stability analysis of differential equations with time-dependent delay. Int. J. Bif. Chaos. 16(2), 465-472 (2006)
3. Li, C.P., Sun, W.G., Kurths, J.: Synchronization of complex dynamical networks with time delays. Physica A 361, 24-34 (2006)
4. Li, C.P., Sun, W.G., Xu, D.: Synchronization of complex dynamical networks with nonlinear inner-coupling functions and time delays. Prog. Theor. Phys. 114(4), 749-761 (2005)
5. Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley-Interscience, New York (1993)
6. Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999)
7. Butzer, P.L., Westphal, U.: An Introduction to Fractional Calculus. World Scientific, Singapore (2000)
8. Agrawal, O.P., Tenreiro Machado, J.A., Sabatier, J.: Introduction. Nonlinear Dyn. 38(1-2), 1-2 (2004)
9. Kempfle, S., Schäfer, I., Beyer, H.: Fractional calculus: theory and applications. Nonlinear Dyn. 29(1-4), 99-127 (2002)
10. Matignon, D.: Stability result on fractional differential equations with applications to control processing. In: Proceedings of IMACS-SMC. pp. 963-968, Lille, France (1996)
11. Chen, Y., Moore, K.L.: Analytical stability bound for a class of delayed fractional-order dynamic systems. Nonlinear Dyn. 29, 191-200 (2002)
12. Muth, E.J.: Transform Methods with Applications to Engineering and Operations Research. Prentice-Hall, New Jersey (1977)
13. Franklin, P.: Functions of Complex Variables. Prentice-Hall, New Jersey (1958)
14. Chen, Y., Moore, K. L.: Analytical stability bound for delayed second-order systems with repeating poles using Lambert function ω. Automatica 38, 891-895 (2002)
15. Deng, W.H., Li, C.P.: Synchronization of chaotic fractional Chen system. J. Phys. Soc. Jpn. 74, 1645-1648 (2005)
16. Deng, W.H., Li, C.P.: Chaos synchronization of the fractional Lu system. Physica A 353, 61-72 (2005)
17. Lu, J.G.: Nonlinear observer design to synchronize fractional-order chaotic system via a scaler transmitted signal. Physica A 359, 107-118 (2005)
18. Lu, J.G.: Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal. Chaos Solitons Fractals 27(2), 519-525 (2006)
19. Zhou, T.S., Li, C.P.: Synchronization in fractional-order differential systems. Physica D 212, 111-125 (2005)
20. Li, C.P., Deng, W.H., Xu, D.: Chaos synchronization of the Chua system with a fractional order. Physica A 360, 171-185 (2006)
21. Diethelm, K., Ford, N.J., Freed, A.D.: A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29(1-4), 3-22 (2002)
22. Li, C.P., Peng, G.J.: Chaos in Chen's system with a fractional order. Chaos Solitons Fractals 22, 443-450 (2004)