Research PapersNo Access

Unstable cycles for the Burke–Shaw system via variational approach

Chengwei Dong

http://orcid.org/0000-0003-4218-2466

Department of Physics, North University of China, Taiyuan 030051, P. R. China

E-mail Address: dongchengwei@tsinghua.org.cn

Corresponding author.

Search for more papers by this author

and

Huihui Liu

Department of Physics, North University of China, Taiyuan 030051, P. R. China

Search for more papers by this author

https://doi.org/10.1142/S0217979219502400Cited by:0 (Source: Crossref)

Abstract

In this paper, the systematical calculations of the unstable cycles for the Burke–Shaw system (BSS) are presented. In contrast to the Poincaré section method used in previous studies, we used the variational method for the cycle search and established appropriate symbolic dynamics on the basis of the topological structure of the cycles. The variational approach made it easy to continuously track the periodic orbits when the parameters were varied. Structure of the whole cycle in the dissipative system demonstrated that the methodology could be effective in most low-dimensional chaotic systems.

Keywords:

PACS: 05.45.-a, 05.45.AC

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963). Web of Science, ADS, Google Scholar
2. O. E. Rössler, Phys. Lett. A. 57, 397 (1976). Web of Science, ADS, Google Scholar
3. G. R. Chen and T. Ueta, Int. J. Bifurcation Chaos 9, 1465 (1999). Link, Web of Science, Google Scholar
4. J. H. Lü and G. R. Chen, Int. J. Bifurcation Chaos 12, 1789 (2002). Link, Web of Science, Google Scholar
5. R. Shaw, Z. Naturforsch. A. 36, 80 (1981). Web of Science, ADS, Google Scholar
6. S. Panchev et al., Chaos Solitons Fractals 33, 1658 (2007). Web of Science, ADS, Google Scholar
7. C. Letellier et al., Phys. Rev. E. 72, 026212 (2005). Web of Science, ADS, Google Scholar
8. C. Letellier et al., J. Phys. A : Gen. Phys. 29, 5359 (1996). ADS, Google Scholar
9. S. H. Strogatz, Nonlinear Dynamics and Chaos : with Applications to Physics, Biology, Chemistry, and Engineering (Hachette, UK, 2014). Google Scholar
10. G. M. Mahmoud et al., Chaos Solitons Fractals 104, 680 (2017). Web of Science, ADS, Google Scholar
11. I. Koyuncu et al., Optoelectron Adv. Mater. 7, 635 (2013). Google Scholar
12. Z. C. Wei et al., Pramana-J. Phys. 90, 50 (2018). Web of Science, ADS, Google Scholar
13. R. Artuso et al., Nonlinearity 3, 325 (1990). Web of Science, ADS, Google Scholar
14. P. Cvitanović et al., Chaos : Classical and Quantum (Niels Bohr Institute, Copenhagen, 2012). Google Scholar
15. B. L. Hao and W. M. Zheng, Applied Symbolic Dynamics and Chaos (World Scientific, Singapore, 1998). Link, Google Scholar
16. Y. Lan and P. Cvitanović, Phys. Rev. E 69, 016217 (2004). Web of Science, ADS, Google Scholar
17. W. H. Press et al., Numerical Recipes in Fortran 77. The Art of Scientific Computing (Cambridge, New York, 1992). Google Scholar
18. C. Dong, Int. J. Mod. Phys. B. 32, 1850227 (2018). Link, Web of Science, ADS, Google Scholar
19. C. Dong, Chinese Phys. B. 27, 080501 (2018). Web of Science, Google Scholar
20. C. W. Dong, Acta Phys. Sin. 67, 240501 (2018). Web of Science, Google Scholar
21. C. Dong, Europhys. Lett. 123, 20005 (2018). ADS, Google Scholar
22. C. Dong, Mod. Phys. Lett. B. 33, 1950212 (2019). Link, Web of Science, ADS, Google Scholar
23. C. Dong and H. Liu, J. Korean Phys. Soc. 75, 188 (2019). Web of Science, Google Scholar
24. C. Dong, Mod. Phys. Lett. B. 32, 1850155 (2018). Link, Web of Science, ADS, Google Scholar
25. C. Dong and Y. Lan, Commun. Nonlinear Sci. Numer. Simul. 19, 2140 (2014). Web of Science, ADS, Google Scholar
26. C. Dong et al., Mod. Phys. Lett. B. 30, 1650183 (2016). Link, Web of Science, ADS, Google Scholar
27. T. D. Tsankov and R. Gilmore, Phys. Rev. Lett. 91, 134104 (2003). Web of Science, ADS, Google Scholar
28. T. D. Tsankov and R. Gilmore, Phys. Rev. E. 69, 056206 (2004). Web of Science, ADS, Google Scholar
29. G. Byrne, R. Gilmore and C. Letellier, Phys. Rev. E. 70, 056214 (2004). Web of Science, ADS, Google Scholar
30. M. Rosalie and C. Letellier, Int. J. Bifurcat. Chaos 24, 1450045 (2014). Link, Web of Science, Google Scholar
31. M. Rosalie, J. Phys. A : Math. Theor. 49, 315101 (2016). Web of Science, Google Scholar