Dynamic analysis of a fractional-order Lorenz chaotic system

Chaos, Solitons and Fractals

Volumn 42, Issue 2, 2009, Pages 1181-1189

  Yu, Yongguang ^a,c   Li, Han Xiong ^b,c   Wang, Sha ^a   Yu, Junzhi ^d  

^a BEIJING JIAOTONG UNIVERSITY   (China)

^b CENTRAL SOUTH UNIVERSITY   (China)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^d INSTITUTE OF AUTOMATION   (China)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS;

ANALYTIC-AND-NUMERICAL METHODS; BIFURCATION CONDITION; DIFFERENTIAL SYSTEMS; EXISTENCE AND UNIQUENESS OF SOLUTION; FRACTIONAL-ORDER CHAOTIC SYSTEMS; INTEGER-ORDER COUNTERPARTS; LORENZ CHAOTIC SYSTEM; NUMERICAL SOLUTION;

CHAOTIC SYSTEMS;

EID: 67649861441     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2009.03.016     Document Type: Article

References (32)

1. Podlubny I. Fractional differential equations (1999), Academic Press, New York
2. Hilfer R. Applications of fractional calculus in physics (2001), World Scientific, New Jersey
3. Bagley R., and Calico R. Fractional order state equations for the control of viscoelastically damped structures. J Guid Contr Dyn 14 (1991) 304-311
4. Sun H., Abdelwahed A., and Onaral B. Linear approximation for transfer function with a pole of fractional order. IEEE Trans Auto Contr 29 (1984) 441-444
5. Ichise M., Nagayanagi Y., and Kojima T. An analog simulation of non-integer order transfer functions for analysis of electrode process. J Electroanal Chem 33 (1971) 253-265
6. Heaviside O. Electromagnetic theory (1971), Chelsea, New York
7. Laskin N. Fractional market dynamics. Physica A 287 (2000) 482-492
8. Kunsezov D., Bulagc A., and Dang G. Quantum levy processes and fractional kinetics. Phys Rev Lett 2 (1999) 1136-1139
9. Laskin N. Fractional quantum mechanics. Phys Rev E 62 (2000) 3135-3145
10. Laskin N. Fractional quantum mechanics and levy path integrals. Phys Lett A 298 (2000) 298-305
11. Laskin N. Fractals and quantum mechanics. Chaos 10 (2000) 780-790
12. Laskin N. Fractional Schrödinger equation. Phys Rev E 66 (2002) 056108
13. Guo X., and Xu M. Some physical applications of fractional Schrödinger equation. J Math Phys 47 (2006) 82104
14. Dong J., and Xu M. Solutions to the space fractional Schrödinger equation using momentum representation method. J Math Phys 48 (2007) 072105
15. Wang S., and Xu M. Generalized fractional Schrödinger equation with space-time fractional derivatives. J Math Phys 48 (2007) 043502
16. Dong J., and Xu M. Space-time fractional Schrödinger equation with time-independent potentials. J Math Anal Appl 344 (2008) 1005-1017
17. Naker M. Time fractional Schrödinger equation. J Math Phys 45 8 (2004) 3339-3352
18. Hartley T., Lorenzo C., and Qammer H. Chaos in a fractional order Chua's system. IEEE Trans Circuit System I 42 (1995) 485-490
19. Li C., and Chen G. Chaos in the fractional order Chen system and its control. Chaos Solitons and Fractals 22 (2004) 549-554
20. Grigorenko I., and Grigorenko E. Chaos dynamics of fractional Lorenz system. Phys Rev Lett 91 (2003) 034101
21. Wang J., and Zhang Y. Designing synchronization schemes for chaotic fractional order unified systems. Chaos Solitons and Fractals 30 (2006) 1265-1272
22. Diethelm K., and Ford J. Analysis of fractional differential equations. J Math Anal Appl 265 (2002) 229-248
23. Lu J. Nonlinear observer design to synchronize fractional-order chaotic systems via a scalar transmitted signal. Physica A 359 (2006) 107-118
24. Yan J., and Li C. On chaos synchronization of fractional differential equations. Chaos Solitons and Fractals 32 (2007) 725-735
25. Wang J., and Zhou T. Chaos synchronization based on contraction principle. Chaos Solitons and Fractals 33 (2007) 163-170
26. Peng G. Synchronization of fractional order chaotic systems. Phys Lett A 363 (2007) 414-419
27. Sweilam N., Khader M., and Al-Bar R. Numerical studies for a multi-order fractional differential equation. Phys Lett A 1-2 (2007) 26-33
28. El-Sayed A., Gaafar F., and Hashem H. On the maximal and minimal solutions of arbitrary orders nonlinear functional integer and differential equations. Math Sci Res J 8 11 (2004) 336-348
29. Ahmad E., El-Sayed A., and El-Saka H. Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models. J Math Anal Appl 325 (2007) 42-553
30. Matignon D. Stability results of fractional differential equations with applications to control processing. In: IMACS. IEEE-SMC: Lille, France; 1996. p. 963-68.
31. Diethelm K., Ford J., and Freed A. Detailed error analysis for a fractional Adams method. Numer Algorithms 36 (2004) 31-52
32. Diethelm K., and Ford J. Multi-order fractional differential equations and their numerical solution. Appl Math Comput 154 (2004) 621-640