Skip to main content
SpringerLink
Log in

On Mathematical Modeling and Analysis of Brain Network

  • Conference paper
  • First Online:
Mathematical Analysis of Continuum Mechanics and Industrial Applications II (CoMFoS 2016)

Part of the book series: Mathematics for Industry ((MFI,volume 30))

Included in the following conference series:

  • 526 Accesses

Abstract

In this article, we first formulate a functional equation-based modeling of the resting-state network, which is attracting attention in the research of the brain. Then, we discuss the local-in-time solvability of the model in a suitable function space.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Cabral, J., Hugues, E., Sporns, O., Deco, G.: Role of local network oscillations in resting-state functional connectivity. NeuroImage 57, 130–139 (2011)

    Article  Google Scholar 

  2. Cabral, J., Kringelbach, M.L., Deco, G.: Exploring the network dynamics underlying brain activity during rest. Prog Neurobiol. 114, 102–131 (2014)

    Article  Google Scholar 

  3. Constantin, A.: A Gronwall-like inequality and its applications. Rend. Mat. Acc. Lincei 9, 111–115 (1990)

    MathSciNet  MATH  Google Scholar 

  4. Constantin, A.: On some integro-differential and integral inequalities and applications, Ann. Univ. Din Timis. Facult. de Mat. Infor. 30, 1–21 (1990)

    Google Scholar 

  5. Deco, G., Jirsa, V., Mclntosh, A.R., Kötter, R.: Key role of coupling, delay and noise in resting brain fluctuations. Proc. Natl. Acad. Sci. U.S.A. 106, 10302–10307 (2009)

    Article  Google Scholar 

  6. Ichinomiya, T.: Frequency synchronization in a random oscillator network. Phys. Rev. E 70, 026116 (2004)

    Article  Google Scholar 

  7. Lavrentiev, M., Spigler, R.S.: Existence and uniqueness of solutions to the Kuramoto-Sakaguchi nonlinear parabolic integrodifferential equation. Differ. Integr. Equ. 13, 649–667 (2000)

    MathSciNet  MATH  Google Scholar 

  8. Lee, W.S., Odd, E., Antonsen, T.M.: Large coupled oscillator systems with heterogeneous interaction delays. Phys. Rev. Lett. 103, 044101 (2009)

    Article  Google Scholar 

  9. Moussa, M.N., Steen, M.R., Laurienti, P.J., Hayasaka, S.: Consistency of network modules in resting-state fMRI connectome data. PLOS One 7, e44428 (2012)

    Article  Google Scholar 

  10. Gusnard, D.A., Raichle, M.E.: Searching for a baseline: functional imaging and the resting human brain. Nat. Rev. Neurosci. 2, 685–694 (2001)

    Article  Google Scholar 

  11. Raichle, M.E., MacLeod, A.M., Snyder, A.Z., Powers, W.J., Gusnard, D.A., Shulman, G.L.: A default mode of brain function. Proc. Natl. Acad. Sci. USA, 98, 676–682

    Google Scholar 

  12. Sjöberg, A.: On the Korteweg-de Vries equation. J. Math. Anal. Appl. 29, 569–579 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  13. Temam, R.: Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 2nd (edn.). Springer, New York (1997)

    Google Scholar 

  14. Tsutsumi, M., Mukasa, T.: Parabolic regularizations for the generalized korteweg-de vries equation. Funkcialaj Ekvacioj 14, 89–110 (1971)

    MathSciNet  MATH  Google Scholar 

  15. Wilson, H.R., Cowan, J.D.: A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13(2), 55–80 (1973)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NTT Network Technology Laboratories, 3-9-11 Midori-Cho, Musashino-Shi, Tokyo, 180-8585, Japan

    Hirotada Honda

Authors
  1. Hirotada Honda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hirotada Honda .

Editor information

Editors and Affiliations

  1. Kanazawa University, Kanazawa, Ishikawa, Japan

    Patrick van Meurs

  2. Kanazawa University, Kanazawa, Ishikawa, Japan

    Masato Kimura

  3. Kanazawa University, Kanazawa, Ishikawa, Japan

    Hirofumi Notsu

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Honda, H. (2018). On Mathematical Modeling and Analysis of Brain Network. In: van Meurs, P., Kimura, M., Notsu, H. (eds) Mathematical Analysis of Continuum Mechanics and Industrial Applications II. CoMFoS 2016. Mathematics for Industry, vol 30. Springer, Singapore. https://doi.org/10.1007/978-981-10-6283-4_14

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-6283-4_14

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-6282-7

  • Online ISBN: 978-981-10-6283-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation