Estimating the Lyapunov exponents of discrete systems

Chaos

Volumn 14, Issue 2, 2004, Pages 343-346

  Li, Changpin ^a,b   Chen, Guanrong ^c  

^a SHANGHAI UNIVERSITY   (China)

^b UNIVERSITY OF PRETORIA   (South Africa)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042600723     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1741751     Document Type: Review

References (32)

1. M. Misiurewicz, Bull. Acad. Polo. Sci. Ser. Sci. Math. 27, 167 (1979).
2. T. Y. Li and J. A. Yorke, Am. Math. Monthly 82, 985 (1975).
3. R. L. Devaney, An Introduction to Chaotic Dynamical Systems (Addison-Wesley, Palo Alto, CA, 1989).
4. T. S. Parker and L. O. Chua, Practical Numerical Algorithms for Chaotic Systems (Springer-Verlag, New York, 1989).
5. R. L. Adler, A. G. Konheim, and M. H. McAndrew, Trans. Am. Math. Soc. 114, 309 (1965).
6. L. S. Block and W. A. Coppl, Dynamics of One Dimension (Springer-Verlag, Berlin, 1992).
7. M. Vellekoop and R. Berglund, Am. Math. Monthly 101, 353 (1994).
8. J. Smital, Trans. Am. Math. Soc. 297, 269 (1986).
9. F. Blanchar, E. Glasner, S. Kolyada, and A. Maass, J. Reine Angew. Math. 547, 51 (2002).
10. F. R. Marotto, J. Math. Anal. Appl. 63, 199 (1978).
11. C. P. Li and G. Chen, Chaos, Solitons Fractals 18, 69 (2003); 20, 655 (2004).
12. C. P. Li and G. Chen, Chaos, Solitons Fractals 18, 69 (2003); 20, 655 (2004).
13. J. Banks and V. Dragan, SIAM Rev. 36, 265 (1994).
14. W. Huang and X. Ye, Topol. Appl. 117, 259 (2002).
15. A. N. Sharkovsky, Ukr. Mat. Zh. 16, 61 (1964).
16. C. H. Hsu and M. C. Li, Am. Math. Monthly 109, 840 (2002).
17. V. I. Oseledec, Trans. Mosc. Math. Soc. 19, 197 (1968).
18. J. Holzfuss and U. Parlitz, Lecture Notes in Mathematics 1486: Lyapunov Exponents, edited by L. Arnold, H. Crauel, and J. P. Eckmann (Springer-Verlag, New York, 1991), p. 263.
19. G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications (World Scientific, Singapore, 1998).
20. Y. S. Xue, Quantitative Study of General Motion Stability and an Example on Power System Stability (Jiangsu Science and Technology, Nanjing, 1999).
21. R. Seydel, From Equilibrium to Chaos: Practical Bifurcation and Stability (Elsevier Science, New York, 1988).
22. R. Bhatia, Matrix Analysis (Springer-Verlag, New York, 1997).
23. C. P. Li and G. Chen, Chaos, Solitons Fractals 18, 809 (2003).
24. C. P. Li, Chaos, Solitons Fractals 21, 855 (2004).
25. J. C. Sprott, http://sprott.physics.wisc.edu/chaos/comchaos.htm
26. T. Erneux and G. Nicolis, Physica D 67, 237 (1993).
27. L. O. Chua and L. Yang, IEEE Trans. Circuits Syst. 35, 1257 (1988).
28. L. O. Chua and L. Yang, IEEE Trans. Circuits Syst. 35, 1273 (1988).
29. T. Roska and L. O. Chua, IEEE Trans. Circuits Syst. 40, 163 (1993).
30. R. L. Winslow, G. B. Ermentrout, and T. L. Williams, Physica D 64, 281 (1993).
31. M. Ding and W. Yang, Phys. Rev. E 56, 4009 (1997).
32. S. Singh, B. Watson, and P. Srivastava, Fixed Point Theory and Best Approximation: The KKM-map Principle (Kluwer Academic, Boston, 1997).