Estimating the ultimate bound and positively invariant set for a new chaotic system and its application in chaos synchronization

Chaos, Solitons and Fractals

Volumn 42, Issue 5, 2009, Pages 2852-2857

  Shu, Yonglu ^a   Xu, Hongxing ^a   Zhao, Yunhong ^a  

^a CHONGQING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; LYAPUNOV FUNCTIONS;

CHAOS SYNCHRONIZATION; GENERALIZED LYAPUNOV FUNCTIONS; ITS APPLICATIONS; NEW CHAOTIC SYSTEMS; POSITIVELY INVARIANT SETS;

SYNCHRONIZATION;

EID: 67651219016     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2009.04.003     Document Type: Article

References (28)

1. Lorenz E.N. Deterministic non-periods flows. J Atmos Sci 20 (1963) 130-141
2. Rösser O.E. An equation for continuous chaos. Phys Lett A 57 (1976) 397-398
3. Matsumoto T. A chaotic attractor from Chua's circuit. IEEE Trans Circ and Syst 31 (1984) 1055-1058
4. Chen G., and Ueta G.T. Yet another chaotic attractor. Int J Bifurc Chaos 9 (1999) 1465-1466
5. Čelikovsý S., and Chen G. On a generalized Lorenz canonical form of chaotic systems. Int J Bifurc Chaos 12 (2002) 1789-1812
6. Ueta T., and Chen G. Bifurcation analysis of Chen's equation. Int J Bifurc Chaos 10 (2000) 1917-1931
7. Chen G., and Lü J. Dynamics of the Lorenz system family: analysis, control and synchronization (2003), Science Press, Beijing [in Chinese]
8. Lü J., and Chen G. A new chaotic attractor coined. Int J Bifurc Chaos 12 (2002) 659-661
9. Lü J., Chen G., Cheng D., and Čelikovsý S. Bridge the gap between the Lorenz system and the Chen system. Int J Bifurc Chaos 12 (2002) 2917-2926
10. Panchev S., Spassova T., and Vitanov N.K. Analytical and numerical investigation of two families of Lorenz-like dynamical systems. Chaos, Solitons & Fractals 33 (2007) 1658-1671
11. Leonov G.A. Bounds for attractors and the existence of homoclinic orbits in the Lorenz system. J Appl Math Mech 65 (2001) 19-32
12. Yu Pogromsky A., Santoboni G., and Nijmeijer H. An ultimate bound on the trajectories of the Lorenz system and its applications. Nonlinearity 16 (2003) 1597-1605
13. Leonov GA, Abramovich SM, Bunin AI. Problems of nonlinear and turbulent process in physics. In: Proc of second international working group, Kiev (in Russian), Part II; 1985. p. 75-77.
14. Leonov G., and Reitmann V. Attraktoreingrenzuny fur Nichtlineare System (1987), Teubner-Verlag, Leipzing
15. Leonov G., Bunin A., and Koksch N. Attractor localization of the Lorenz system. ZAMM 67 (1987) 649-656
16. Peter S.-D. Bounds for trajectories of the Lorenz equations:an illustration of how to choose Liapunov functions. Phys Lett A 281 (2001) 161-167
17. Liao X.X., Fu Y.L., and Xie S.L. On the new results of global attractive set and positive invariant set of the Lorenz chaotic system and the applications to chaos control and synchronization. Sci China Ser F Inform Sci 48 (2005) 304-321
18. Li D., Lu J., Wu X., and Chen G. Estimating the bounds for the Lorenz family of chaotic systems. Chaos, Solitons & Fractals 23 (2005) 529-534
19. Li D., Lu J., Wu X., and Chen G. Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system. J Math Anal Appl 323 (2006) 844-853
20. Yu P., and Liao X.X. New estimations for globally attractive and positive invariant set of the family of the Lorenz system. Int J Bifurc Chaos 16 (2006) 3383-3390
21. Yu P., and Liao X.X. New estimations for globally attractive and positive invariant set of the family of the Lorenz systems. Int J Bifurc Chaos 11 (2006) 3383-3390
22. Sun Y.J. Solution bounds of generalized Lorenz chaotic systems. Chaos, Solitons & Fractals 40 (2009) 691-696
23. Qin W.X., and Chen G. On the boundedness of solutions of the Chen system. J Math Anal Appl 329 (2007) 445-451
24. Yu P., and Liao X.X. On the study of globally exponentially attractive set of a general chaotic system. Commun Nonlinear Sci Numer Simulat 13 (2008) 1498-1507
25. Liao X.X., and Yu P. Study on the global property of the smooth Chua's system. Int J Bifurc Chaos 16 (2006) 2815-2841
26. Li D., Lu J., and Wu X. Estimating the ultimate bound and positively invariant set for the hyperchaotic Lorenz-Haken system. Chaos, Solitons & Fractals 39 (2009) 1290-1296
27. Chu Y.D., and Li X.F. Computer simulation and circuit implementation for a new autonomous chaotic system. J Sichuan Univ 44 (2007) 596-602 [in Chinese]
28. Lefchetz S. Differential equations: geometric theory (1963), Interscience, New York