Abstract
In this paper, we present an analytical study on the synchronization dynamics observed in unidirectionally-coupled quasiperiodically-forced systems that exhibit strange non-chaotic attractors (SNA) in their dynamics. The SNA dynamics observed in the uncoupled system is studied analytically through phase portraits and Poincare maps. A difference system is obtained by coupling the state equations of similar piecewise linear regions of the drive and the response systems. The mechanism of synchronization of the coupled system is realized through the bifurcation of the eigenvalues in one of the piecewise linear regions of the difference system. The analytical solutions obtained for the normalized state equations in each piecewise linear region of the difference system have been used to explain the synchronization dynamics through phase portraits and time-series analysis. The stability of the synchronized state is confirmed through the master stability function. An explicit analytical solution explaining the synchronization of SNAs is reported in the literature for the first time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Grebogi et al., Physica D 13, 261 (1984).
J. F. Heagy and S. M. Hammel, Physica D 70, 140 (1994).
A. Venkatesan et al., Phys. Rev. E 61, 3641 (2000).
A. Prasad et al., Int. J. Bif. Chaos 11, 291 (2001).
M. Agarwal et al., Phys. Rev. E 81, 026202 (2010).
K. Srinivasan et al., Int. J. Bif. Chaos 19, 4131 (2009).
K. Thamilmaran et al., Phys. Rev. E 74, 036205 (2006).
A. Venkatesan, K. Murali and M. Lakshmanan, Phys. Lett. A 259, 246 (1999).
Z. Liu and Z. Zhu, Int. J. Bif. Chaos 6, 1383 (1996).
A. Arulgnanam et al., Chaos Solitons Fract. 75, 96 (2015).
A. Arulgnanam et al., Int. J. Bif. Chaos 25, 1530020 (2015).
G. Sivaganesh et al., J. Korean Phys. Soc. 69, 124 (2016).
G. Sivaganesh, Chin. J. Phys. 52, 1760 (2014).
M. Pecora and L. Carroll, Phys. Rev. Lett. 64, 821 (1990).
M. Pecora and L. Carroll, IEEE Trans. Circ. Syst. 38, 453 (1991).
M. Pecora et al., Chaos 7, 520 (1997).
M. Pecora and L. Carroll, Phys. Rev. Lett. 80, 2109 (1998).
M. Pecora and L. Carroll, Int. J. Bif. Chaos 9, 2315 (1999).
L. Huang, Q. Chen, Y. C. Lai and M. Pecora, Phys. Rev. E 80, 036204 (2009).
G. Sivaganesh, J. Korean Phys. Soc. 68, 628 (2016).
G. Sivaganesh, Chin. Phys. Lett. 32, 010503 (2015).
P. R. Venkatesh et al., Pramana 86, 1195 (2016).
R. Ramasamy, Phys. Rev. E 56, 7294 (1997).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sivaganesh, G., Arulgnanam, A. An analytical study on the synchronization of strange non-chaotic attractors. Journal of the Korean Physical Society 69, 1631–1637 (2016). https://doi.org/10.3938/jkps.69.1631
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3938/jkps.69.1631