Advertisement

Rich Dynamics Induced by Synchronization Varieties in the Coupled Thalamocortical Circuitry Model

  • Denggui Fan
  • Jianzhong Su
  • Ariel Bowman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11309)

Abstract

Epileptic disorders are typically characterized by the synchronous spike-wave discharges (SWD). However, the mechanism of SWD is not well-understood in terms of its synchronous spatio-temporal features. In this paper, based on the coupled thalamocortical (TC) neural field models we first investigate the SWD complete synchronization (CS), lag synchronization (LS) and anticipated synchronization (AS) mainly using the adaptive delayed feedback (ADF) and active control (AC). Then we explore the dynamics of 3-compartment coupled TC motifs with the interactive connectivity patterns of ADF and AC, as well as the various interactive weights. It is found that CS, LS and AS of motifs can coexist and transit between each other by changing the various interactive modes and weights. These results provide the complementary synchronization effects and conditions for the basic 3-node motifs. This may facilitate to construct the architecture based on patient EEG data and reveal the abnormal information expression of epileptic oscillatory network.

Keywords

Spike-wave discharges (SWD) Synchronization control Adaptive feedback control Active control Network motifs 

References

  1. 1.
    Suffczynski, P., Kalitzin, S., Da Silva, F.L.: Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network. Neuroscience 126(2), 467–484 (2004)CrossRefGoogle Scholar
  2. 2.
    Lytton, W.W., et al.: Dynamic interactions determine partial thalamic quiescence in a computer network model of spike-and-wave seizures. J. Neurophysiol. 77(4), 1679–1696 (1997)CrossRefGoogle Scholar
  3. 3.
    Taylor, P.N., et al.: A computational study of stimulus 1186 driven epileptic seizure abatement. PLoS One 9(12), e114316 (2014)CrossRefGoogle Scholar
  4. 4.
    Rosenblum, M.G., et al.: From phase to lag synchronization in coupled chaotic oscillators. Phys. Rev. Lett. 78(22), 4193 (1997)CrossRefGoogle Scholar
  5. 5.
    Yan, Z.: A new scheme to generalized (lag, anticipated, and complete) synchronization in chaotic and hyperchaotic systems. Chaos 15(1), 13101 (2005)MathSciNetCrossRefGoogle Scholar
  6. 6.
    LaSalle, J.: Some extensions of Liapunov’s second method. IRE Trans. Circ. Theory 7(4), 520–527 (1960)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Hale, J.K.: Dynamical systems and stability. J. Math. Anal. Appl. 26(1), 39–59 (1969)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Voss, H.U.: Anticipating chaotic synchronization. Phys. Rev. E 61(5), 5115 (2000)CrossRefGoogle Scholar
  9. 9.
    Milo, R., et al.: Network motifs: simple building blocks of complex networks. Science 298(5594), 824–827 (2002)CrossRefGoogle Scholar
  10. 10.
    Sporns, O., Kotter, R.: Motifs in brain networks. PLoS Biol. 2(11), e369 (2004)CrossRefGoogle Scholar
  11. 11.
    Battiston, F., et al.: Multilayer motif analysis of brain networks. Chaos Interdiscip. J. Nonlinear Sci. 27(4), Article no. 047404 (2017)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Gollo, L.L., Breakspear, M.: The frustrated brain: from dynamics on motifs to communities and networks. Phil. Trans. R. Soc. B 369(1653), Article no. 20130532 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Mathematics and PhysicsUniversity of Science and Technology BeijingBeijingChina
  2. 2.Department of MathematicsUniversity of Texas at ArlingtonArlingtonUSA

Personalised recommendations