Abstract
A system of Hindmarsh-Rose relay neurons with time delay coupling is considered in which the relay (central) neuron has an additional feedback term that represents the interaction activity with a local environment. The strength of environmental coupling with the central neuron plays an important role in inducing synchronization and de-synchronization between the outer neurons. The strength of feedback developed from the environmental coupling has created a gradual quenching in the oscillations of the central neuron. At a higher feedback coupling strength, oscillation of the central neuron is suppressed drastically and a transition from a regime of synchronization to out-of-phase synchronization take place between the oscillations of the two outer neurons.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization, A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2001)
E. Rodriguez, N. George, J.P. Lachaux, J. Martinerie, B. Renault, F.J. Varela, Nature 397, 430 (1999)
W.H.R. Miltner, C. Braun, M. Arnold, H. Witte, E. Taub, Nature 397, 434, (1999)
A.K. Engel, P. König, A.K. Kreiter, T.B. Schillen, W. Singer, Trends Neurosci. 15, 218 (1992)
U.S. Thounaojam, K. Manchanda, R. Ramaswamy, A. Bose, SIAM J. Appl. Dyn. Syst. 10, 987 (2011)
B.B. Theyel, D.A. Llano, M. Sherman, Nat. Neurosci. 13, 84 (2010)
L.L. Gollo, C.R. Mirasso, M. Atienza, M. Crespo-Garcia, J.L. Cantero, PLoS ONE 6(3), 17756 (2011)
I. Fischer, R. Vicente, J.M. Buldú, M. Peil, C.R. Mirasso, M.C. Torrent, J.G. Ojalvo, Phys. Rev. Lett. 97, 123902(4) (2006)
F.M. Atay (ed.), Complex Time-Delay Systems (Springer-Verlag, Berlin, 2010)
H.G. Schuster, P. Wagne, Prog. Theor. Phys. 81, 939 (1989)
F.M. Atay, J. Jost, A. Wende, Phys. Rev. Lett. 92, 144101(4) (2004)
G. Saxena, A. Prasad, R. Ramaswamy, Phys. Rep. 521, 205 (2012)
A. Prasad, M. Dhamala, B.M. Adhikari, R. Ramaswamy, Phys. Rev. E 81, 027201 (2010)
D.V.R. Reddy, A. Sen, G.L. Johnston, Phys. Rev. Lett. 80, 5109(4) (1998)
D.V.R. Reddy, A. Sen, G. L. Johnston, Phys. Rev. Lett. 85, 3381(4) (2000)
F.M. Atay, Physica D 183, 1 (2003)
D.J. Selkoe, Ann. N. Y. Acad. Sci. 924, 17 (2000)
F. Toschi, F. Lugli, F. Biscarini, F. Zerbetto, J. Phys. Chem. 113, 369 (2009)
P.R. Sharma, A. Sharma, M.D. Shrimali, A. Prasad, Phys. Rev. E 83, 067201 (2011)
J.L. Hindmarsh, R.M. Rose, Proc. R. Soc. Lond. B 221, 87 (1984)
K. Pyragas, Phys. Lett. A 170, 421 (1992)
K. Pyragas, Phil. Trans. R. Soc. A 364, 2309 (2006)
J.D. Farmer, Physica D 4(3), 366 (1984)
M. Dhamala, V.K. Jirsa, M. Ding, Phys. Rev. Lett. 92, 074104(4) (2004)
A. Bergner, M. Frasca, G. Sciuto, A. Buscarnino, E.J. Ngamga, L. Fortuna, J. Kurths, Phy. Rev. E 85, 026208 (2012)
Z. Ma, G. Zhang, Y. Wang, Z. Liu, J. Phys. A: Math. Theor. 41, 155101 (2008)
L. Chandrasekaran, S. Achuthan, C. Canavier Carmen, J. Comput. Neurosci. 30, 427 (2011)
S. Achuthan, C. Canavier Carmen, J. Neurosci. 29(16), 5218 (2009)
S.J.S. Theesar, M.R.K. Ariffin, S. Banerjee, Optics Laser Technol. 54, 15 (2013)
D.G. Aronson, G.B. Ermentrout, N. Kopell, Physica D 41, 403 (1990)
J.J. Collins, I.N. Stewart, J. Nonlin. Sci. 3, 349 (1993)
P.J. Uhlhaas, D.E.J. Linden, W. Singer, C. Haenschel, M. Lindner, K. Maurer, E. Rodriguez, J. Neuerosci. 26, 8168 (2006)
M.W. Howe, H.E. Atallah, A. McCool, D.J. Gibson, A.M. Graybiel, PNAS 108, 16801 (2011)
L. Appeltant, G.V. Sande, J. Danckaert, I. Fischer, Nat. Sci. Reports 4, 3629(1–5) (2014)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Thounaojam, U., Sharma, P. & Shrimali, M. Phase switching in Hindmarsh-Rose relay neurons. Eur. Phys. J. Spec. Top. 225, 17–27 (2016). https://doi.org/10.1140/epjst/e2016-02612-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2016-02612-1