Generating multi-directional multi-scroll chaotic attractors via a fractional differential hysteresis system

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 369, Issue 5-6, 2007, Pages 438-443

  Deng, Weihua ^a,b   Lü, Jinhu ^c,d  

^a LANZHOU UNIVERSITY   (China)

^b SHANGHAI UNIVERSITY   (China)

^c CHINESE ACADEMY OF SCIENCES   (China)

^d WUHAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

HYSTERESIS;

CHAOTIC ATTRACTORS; DYNAMICAL MECHANISMS; FRACTIONAL DIFFERENTIAL; HYSTERESIS SYSTEM; MULTISCROLL CHAOTIC ATTRACTOR;

DYNAMICAL SYSTEMS;

EID: 34548617848     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2007.04.112     Document Type: Article

References (42)

1. Oldham K.B., and Spanier J. The Fractional Calculus (1974), Academic Press, New York
2. Kenneth S.M., and Bertram R. An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), Wiley-Interscience, USA
3. Podlubny I. Fractional Differential Equations (1999), Academic Press, New York
4. Butzer P.L., and Westphal U. An Introduction to Fractional Calculus (2000), World Scientific, Singapore
5. Mainardi F. Fractional calculus. In: Carpinteri A., and Mainardi F. (Eds). Fractals and Fractional Calculus in Continuum Mechanics (1997), Springer, New York
6. Gorenflo R., and Vessella S. Abel Integral Equations: Analysis and Applications (1991), Springer, New York
7. Agrawal O.P., Tenreiro Machado J.A., and Sabatier J. Nonlinear Dynam. 38 (2004) 1
8. Koeller R.C. J. Appl. Mech. 51 (1984) 229
9. Mandelbrot B. IEEE Trans. Inform. Theory 13 (1967) 289
10. Sugimoto N. J. Fluid Mech. 225 (1991) 631
11. Heaviside O. Electromagnetic Theory (1971), Chelsea, New York
12. Kusnezov D., Bulgac A., and Dang G.D. Phys. Rev. Lett. 82 (1999) 1136
13. Zaslavsky G.M. Phys. Rep. 371 (2002) 461
14. Mainardi F. Chaos Solitons Fractals 7 (1996) 1461
15. Ichise M., Nagayanagi Y., and Kojima T. J. Electroanal. Chem. 33 (1971) 253
16. Chua L.O., Komuro M., and Matsumoto T. IEEE Trans. Circuits Syst. CAS-33 (1986) 1073
17. Chua L.O. Int. J. Circuit Theor. Appl. 22 (1994) 279
18. Madan R.N. Chua's Circuit: A Paradigm for Chaos (1993), World Scientific, Singapore
19. Suykens J.A.K., and Vandewalle J. IEEE Trans. Circuits Systems I 40 (1993) 861
20. Yalcin M.E., Suykens J.A.K., Vandewalle J., and Ozoguz S. Int. J. Bifur. Chaos 12 (2002) 23
21. Yalcin M.E., Suykens J.A.K., and Vandewalle J. Cellular Neural Networks, Multi-Scroll Chaos and Synchronization (2005), World Scientific, Singapore
22. Lü J.H., Yu X., and Chen G. IEEE Trans. Circuits Systems I 50 (2003) 198
23. Lü J.H., Han F., Yu X., and Chen G. Automatica 40 (2004) 1677
24. Lü J.H., Yu S.M., Leung H., and Chen G. IEEE Trans. Circuits Systems I 53 (2006) 149
25. Lü J.H., and Chen G. Int. J. Bifur. Chaos 16 (2006) 775
26. Matignon D. Computational Engineering in Systems and Application Multiconference vol. 2 (1996), IMACS, IEEE-SMC, Lille, France 963
27. Deng W.H., Li C.P., and Lü J.H. Nonlinear Dynam. 48 (2007) 409
28. Hartley T.T., Lorenzo C.F., and Qammer H.K. IEEE Trans. Circuits Systems I Fund. Theory Appl. 42 (1995) 485
29. Ahmad W.M., and Sprott J.C. Chaos Solitons Fractals 16 (2003) 339
30. Grigorenko I., and Grigorenko E. Phys. Rev. Lett. 91 (2003) 034101
31. Grigorenko I., and Grigorenko E. Phys. Rev. Lett. 96 (2006) 199902
32. Li C.G., Liao X.F., and Yu J.B. Phys. Rev. E 68 (2003) 067203
33. Deng W.H. Phys. Rev. E 75 (2007) 056201
34. Deng W.H., and Li C.P. J. Phys. Soc. Jpn. 74 (2005) 1645
35. Deng W.H., and Li C.P. Physica A 353 (2005) 61
36. Li C.P., Deng W.H., and Xu D. Physica A 360 (2006) 171
37. Ahmad W. Chaos Solitons Fractals 25 (2005) 727
38. Ahmad W. Chaos Solitons Fractals 27 (2006) 1213
39. Deng W.H. Int. J. Bifur. Chaos Appl. Sci. Eng. 17 (2007) in press
40. Deng W.H., and Lü J.H. Chaos 16 (2006) 043120
41. Diethelm K., Ford N.J., and Freed A.D. Nonlinear Dynam. 29 (2002) 3
42. Deng W.H. J. Comput. Appl. Math. 206 (2007) 174