Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system

Journal of Mathematical Analysis and Applications

Volumn 323, Issue 2, 2006, Pages 844-853

  Li, Damei ^a   Lu, Jun an ^a   Wu, Xiaoqun ^a   Chen, Guanrong ^b  

^a WUHAN UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Lorenz system; Lyapunov function; Positively invariant set; Ultimate bound; Unified chaotic system

Indexed keywords

EID: 33750606677     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.11.008     Document Type: Article

References (14)

1. Lorenz E.N. Deterministic non-periods flows. J. Atoms Sci. 20 (1963) 130-141
2. Chen G., and Ueta T. Yet another chaotic attractor. Int. J. Bifur. Chaos 9 (1999) 1465-1466
3. Vaněcěk A., and Cělikovesky S. Control Systems: From Linear Analysis to Synthesis of Chaos (1996), Prentice Hall, London
4. Lü J., and Chen G. A new chaotic attractor coined. Int. J. Bifur. Chaos 12 (2002) 659-661
5. Lü J., Chen G., Cheng D., and Čelikovsky̌ S. Bridge the gap between the Lorenz system and the Chen system. Int. J. Bifur. Chaos 12 (2002) 2917-2926
6. Chen G., and Lü J. Dynamical Analysis, Control and Synchronization of the Lorenz Systems Family (2003), Science Press, China
7. Lu J., Wu X., and Lü J. Synchronization of a unified chaotic system and the application in secure communication. Phys. Lett. A 305 (2002) 365-370
8. Leonov G. Bound for attractors and the existence of homoclinic orbit in the Lorenz system. J. Appl. Math. Mech. 65 (2001) 19-32
9. Zhou T., Tang Y., and Chen G. Complex dynamical behaviors of the chaotic Chen's system. Int. J. Bifur. Chaos 9 (2003) 2561-2574
10. Pogromsky A., Santoboni G., and Nijmeijer H. An ultimate bound on the trajectories of the Lorenz systems and its applications. Nonlinearity 16 (2003) 1597-1605
11. Leonov G., Bunin A., and Koksch N. Attractor localization of the Lorenz system. Z. Angew. Math. Mech. 67 (1987) 649-656
12. 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
13. Liao X. On the global basin of attraction and positively invariant set for the Lorenz chaotic system and its application in chaos control and synchronization. Sci. China Ser. E 34 (2004) 1404-1419
14. Lefchetz S. Differential Equations: Geometric Theory (1963), Interscience, New York