Abstract
In this paper, we numerically study the stochastic and the deterministic occasional uncoupling methods of effecting identical synchronized states in low dimensional, dissipative, diffusively coupled, chaotic flows that are otherwise not synchronized when continuously coupled at the same coupling strength parameter. In the process of our attempt to understand the mechanisms behind the success of the occasional uncoupling schemes, we devise a hybrid between the transient uncoupling and the stochastic on-off coupling, and aptly name it the transient stochastic uncoupling – yet another stochastic occasional uncoupling method. Our subsequent investigation on the transient stochastic uncoupling allows us to surpass the effectiveness of the stochastic on-off coupling with very fast on-off switching rate. Additionally, through the transient stochastic uncoupling, we establish that the indicators quantifying the local contracting dynamics in the corresponding transverse manifold are generally not useful in finding the optimal coupling region of the phase space in the case of the deterministic transient uncoupling. In fact, we highlight that the autocorrelation function – a non-local indicator of the dynamics – of the corresponding response system’s chaotic time-series dictates when the deterministic uncoupling could be successful. We illustrate all our heuristic results using a few well-known examples of diffusively coupled chaotic oscillators.
Graphical abstract
Similar content being viewed by others
References
S.H. Strogatz,Sync: The emerging science of spontaneous order, 1st edn. (Hyperion press, New York, 2003)
A.T. Winfree, J. Theor. Biol. 16, 15 (1967)
I. Aihara, H. Kitahata, K. Yoshikawa, K. Aihara, Artif. Life Robot. 12, 29 (2008)
E. Montbrió, D. Pazó, A. Roxin, Phys. Rev. X 5, 021028 (2015)
H.G. Winful, L. Rahman, Phys. Rev. Lett. 65, 1575 (1990)
R. Roy, K.S. Thornburg, Phys. Rev. Lett. 72, 2009 (1994)
A.E. Motter, S.A. Myers, M. Anghel, T. Nishikawa, Nat. Phys. 9, 191 (2013)
K. Wiesenfeld, P. Colet, S.H. Strogatz, Phys. Rev. Lett. 76, 404 (1996)
S.A. Pawar, A. Seshadri, V.R. Unni, R.I. Sujith, J. Fluid Mech. 827, 664 (2017)
L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990)
L.M. Pecora, T.L. Carroll, G.A. Johnson, D.J. Mar, J.F. Heagy, Chaos 7, 520 (1997)
A. Pikovsky, M. Rosenblum, J. Kurths,Synchronization: A universal concept in nonlinear sciences, 1st edn. (Cambridge University Press, New York, 2001)
S. Boccaletti, J. Kurths, G. Osipov, D.L. Valladares, C.S. Zhou, Phys. Rep. 366, 1 (2002)
A. Balanov, N. Janson, D. Postnov, O. Sosnovtseva,Synchronization: From Simple to Complex, 1st edn. (Springer Press, Berlin, 2008)
A. Hampton, D.H. Zanette, Phys. Rev. Lett. 83, 2179 (1999)
S. Sur, A. Ghosh, Phys. Lett. A 384, 126176 (2020)
H. Qiu, B. Juliá-Díaz, M.A. Garcia-March, A. Polls, Phys. Rev. A 90, 033603 (2014)
J. Tian, H. Qiu, G. Wang, Y. Chen, L. Fu, Phys. Rev. E 88, 032906 (2013)
H. Qiu, R. Zambrini, J. Juliá-Díaz, B. Polls, A. Martorell, Phys. Rev. A 92, 043619 (2015)
F. Bemani, A. Motazedifard, R. Roknizadeh, M.H. Naderi, D. Vitali, Phys. Rev. A 96, 023805 (2017)
T. Stojanovski, L. Kocarev, U. Parlitz, Phys. Rev. E 54, 2128 (1996)
M. Zochowski, Physica D 145, 181 (2000)
L. Chen, C. Qiu, H.B. Huang, Phys. Rev. E 79, 045101 (2009)
R. Jeter, I. Belykh, IEEE Trans. Circuits Syst. I 62, 1260 (2015)
M. Schröder, M. Mannattil, D. Dutta, S. Chakraborty, M. Timme, Phys. Rev. Lett. 115, 054101 (2015)
S. Li, N. Sun, L. Chen, X. Wang, Phys. Rev. E 98, 012304 (2018)
A. Hagberg, D.A. Schult, Chaos 18, 037105 (2008)
L. Chen, C. Qiu, H.B. Huang, G.X. Qi, H.J. Wang, Eur. Phys. J. B 76, 625 (2010)
A. Kumar, V. Agrawal, S. Sinha, Eur. Phys. J. B 88, 138 (2015)
M. Schröder, S. Chakraborty, D. Witthaut, J. Nagler, M. Timme, Sci. Rep. 6, 37142 (2016)
J. Zhou, Y. Zou, S. Guan, Z. Liu, S. Boccaletti, Sci. Rep. 6, 35979 (2016)
R. Jeter, M. Porfiri, I. Belykh, Chaos 28, 071104 (2018)
S. Nag Chowdhury, D. Ghosh, Europhys. Lett. 125, 10011 (2019)
A. Gomez-Marin, J. Garcia-Ojalvo, J.M. Sancho, Phys. Rev. Lett. 98, 168303 (2007)
P.C. Bressloff, S.D. Lawley, J. Nonlinear Sci. 27, 1487 (2017)
J. Gou, W. Chiang, P. Lai, M.J. Ward, Y. Li, Physica D 339, 1 (2017)
A. Tandon, M. Schröder, M. Mannattil, M. Timme, S. Chakraborty, Chaos 26, 094817 (2016)
A. Ghosh, P. Godara, S. Chakraborty, Chaos 28, 053112 (2018)
A. Ghosh, T. Shah, S. Chakraborty, Chaos 28, 123113 (2018)
R. Jeter, I. Belykh, Dynamical networks with on-off stochastic connections: Beyond fast switching, in2014 IEEE International Symposium on Circuits and Systems (ISCAS), 2014, p. 1788
O. Golovneva, R. Jeter, I. Belykh, M. Porfiri, Physica D 340, 1 (2017)
M. Porfiri, I. Belykh, SIAM J. Appl. Dyn. Syst. 16, 1372 (2017)
P.S. Landa, P.V.E. McClintock, J. Phys. A 33, L433 (2000)
T. Stojanovski, L. Kocarev, U. Parlitz, R. Harris, Phys. Rev. E 55, 4035 (1997)
I.V. Belykh, V.N. Belykh, M. Hasler, Physica D 195, 188 (2004)
S. Boccaletti, C. Grebogi, Y.C. Lai, H. Mancini, D. Maza, Phys. Rep. 329, 103 (2000)
M.P. Juniper, R.I. Sujith, Annu. Rev. Fluid Mech. 50, 661 (2018)
S.C. Fisher, S.A. Rahman, NASA History Division, Remembering the Giants: Apollo Rocket Propulsion Development. Monographs in aerospace history, National Aeronautics and Space Administration, NASA History Division, Office of External Relations, 2009
P.L. Rijke, Lond. Edinb. Dubl. Philos. Mag. 17, 419 (1859)
N. Thomas, S. Mondal, S.A. Pawar, R.I. Sujith, Chaos 28, 033119 (2018)
E.R. Hunt, Phys. Rev. Lett. 67, 1953 1991
V. Petrov, B. Peng, K. Showalter, J. Chem. Phys. 96, 7506 (1992)
A. Garfinkel, M.L. Spano, W.L. Ditto, J.N. Weiss, Science 257, 1230 (1992)
T. Maiwald, E. Mammen, S. Nandi, J. Timmer, inSurrogate Data — A Qualitative and Quantitative Analysis (Springer, Berlin, 2008), p. 41
G. Lancaster, D. Iatsenko, A. Pidde, V. Ticcinelli, A. Stefanovska, Phys. Rep. 748, 1 (2018)
H. Kantz, T. Schreiber,Nonlinear Time Series Analysis, 2nd edn. (Cambridge University Press, New York, 2004)
E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)
A. Stefański, P. Perlikowski, T. Kapitaniak, Phys. Rev. E 75, 016210 (2007)
O.E. Rössler, Phys. Lett. A 57, 397 (1976)
J.-M. Malasoma, Phys. Lett. A 264, 383 (2000)
J.C. Sprott,Chaos and Time-Series Analysis, 1st edn. (Oxford University Press, New York, 2003)
G. Chen, T. Ueta, Int. J. Bifurc. Chaos 09, 1465 (1999)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ghosh, A., Chakraborty, S. Comprehending deterministic and stochastic occasional uncoupling induced synchronizations through each other. Eur. Phys. J. B 93, 113 (2020). https://doi.org/10.1140/epjb/e2020-100580-7
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2020-100580-7