Fractional-order attractors synthesis via parameter switchings

Communications in Nonlinear Science and Numerical Simulation

Volumn 15, Issue 12, 2010, Pages 3745-3753

  Danca, Marius F ^a,b   Diethelm, Kai ^c,d  

^a Avram Iancu University   (Romania)

^b TECHNICAL UNIVERSITY OF CLUJ NAPOCA   (Romania)

^c TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

^d GNS Gesellschaft für Numerische Simulation mbH Am Gaußberg 2   (Germany)

Author keywords

Caputo derivative; Chaotic attractor; Fractional differential equation; Fractional L system; Numerical methods

Indexed keywords

COMPUTER CONTROL SYSTEMS; DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS;

CAPUTO DERIVATIVES; CHAOTIC ATTRACTORS; CONTROL PARAMETERS; DETERMINISTICS; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL LÜ SYSTEM; FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; NUMERICAL EVIDENCE; PARAMETER SWITCHING;

NUMERICAL METHODS;

EID: 77952742223     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.01.011     Document Type: Article

References (29)

1. Danca M.-F., Tang W.K.S., and Chen G. A switching scheme for synthesizing attractors of dissipative chaotic systems. Appl Math Comput 201 (2008) 650-667
2. Danca M.-F. Random parameter-switching synthesis of a class of hyperbolic attractors. Chaos 18 (2008) 033111
3. Lu J.G. Chaotic dynamics of the fractional-order Lü system and its synchronization. Phys Lett A 354 (2006) 305-311
4. Hirsch M., and Pugh C. Stable manifolds and hyperbolic sets. Proc Sympos Pure Math 14 (1970) 133-164
5. Hirsch W.M., Smale S., and Devaney L.R. Differential equations dynamical systems and an introduction to chaos. 2nd ed. (2004), Elsevier, Amsterdam
6. Kapitanski L., and Rodnianski I. Shape and Morse theory of attractors. Commun Pure Appl Math 53 (2000) 218-242
7. Temam R. Infinite dimensional dynamical systems in mechanics and physics (1988), Springer, Berlin
8. Foias C., and Jolly M.S. On the numerical algebraic approximation of global attractors. Nonlinearity 8 (1995) 95-319
9. Milnor J. On the concept of attractor. Commun Math Phys 99 (1985) 177-195
10. Podlubny I. Fractional differential equations (1999), Academic Press, San Diego
11. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional integrals and derivatives (1999), Gordon and Breach, Yverdon
12. Ahmed E., and Elgazzar A.S. On fractional order differential equations model for nonlocal epidemics. Physica A 379 (2007) 607-614
13. Chen W. Nonlinear dynamics and chaos in a fractional-order financial system. Chaos, Solitons & Fractals 36 (2008) 1305-1314
14. El-Sayed A.M.A., El-Mesiry A.E.M., and El-Saka H.A.A. On the fractional-order logistic equation. Appl Math Lett 20 (2007) 817-823
15. In: Hilfer R. (Ed). Applications of fractional calculus in physics (2001), World Scientific, New Jersey
16. Kiani B.A., Fallahi K., Pariz N., and Leung H. A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter. Commun Nonlinear Sci Numer Simul 14 (2009) 863-879
17. Laskin N. Fractional market dynamics. Physica A 287 (2000) 482-492
18. Oustaloup A. La Dérivation Non Entière: Théorie, Synthèse et Applications (Hermes, Paris); 1995.
19. Podlubny I., Petráš I., Vinagre B.M., O'Leary P., and Dorcák L. Analogue realization of fractional-order controllers. Nonlinear Dynam 29 (2002) 281-296
20. Sun H.H., Abdelwahab A.A., and Onaral B. Linear approximation of transfer function with a pole of fractional order. IEEE Trans Automat Contr 29 (1984) 441-444
21. Diethelm K., Ford N.J., and Freed A.D. A predictor-corrector approach for the numerical solution of fractional differential equations. Nonlinear Dynam 29 (2002) 3-22
22. Diethelm K., Ford N.J., and Freed A.D. Detailed error analysis for a fractional Adams method. Numer Algorithms 36 (2004) 31-52
23. Tavazoei M.S. Comments on stability analysis of a class of nonlinear fractional-order systems. IEEE Trans Circ Syst II 56 (2009) 519-520
24. Tavazoei M.S., Haeri M., Bolouki S., and Siami M. Stability preservation analysis for frequency-based methods in numerical simulation of fractional-order systems. SIAM J Numer Anal 47 (2008) 321-338
25. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical recipes in C: the art of scientific computing. 2nd ed. (1992), Cambridge University Press, Cambridge
26. Petráš I. Chaos in the fractional-order Volta's system: modeling and simulation. Nonlinear Dynam 57 (2009) 157-170
27. Hartley T.T., Lorenzo C.F., and Killory Qammar H. Chaos in a fractional order Chua's system. IEEE Trans Circ Syst I 42 (1995) 485-490
28. Lü J., Chen G., Cheng D., and Celikovsky S. Bridge the gap between the Lorenz system and the Chen system. Int J Bifurcat Chaos 12 (2002) 2917-2926
29. Falconer K. Fractal geometry: mathematical foundations and applications (1990), John Wiley & Sons, Chichester