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Dergiler / Sakarya University Journal of Science / 2026 / Volume: 24 Issue: 1

Stability Switches of A Neural Field Model: An Algebraic Study On The Parameters

Berrak Özgür(İZMİR DEMOCRACY UNIVERSITY)0000-0002-9709-7376
Sayfa
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Yayın Tarihi
2020-02-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Using Routh-Hurwitz criterion, some conditions for characteristic equation are given for the stability of the system.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, a special case for a delayed neural field model is considered.
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Temel Bulgular & Veri:After constructing its characteristic equation a stability analysis is made.
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Sonuç & Katkı:Using Routh-Hurwitz criterion, some conditions for characteristic equation are given for the stability of the system.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:delay differential equations · characteristic equation · stability analysis

Abstract

In this paper, a special case for a delayed neural field model is considered. After constructing its characteristic equation a stability analysis is made. Using Routh-Hurwitz criterion, some conditions for characteristic equation are given for the stability of the system.

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Bu Makaleye Atıf Yap

Özgür, B. (2020). Stability Switches of A Neural Field Model: An Algebraic Study On The Parameters. Sakarya University Journal of Science, Volume: 24 Issue: 1. https://doi.org/10.16984/saufenbilder.521545

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Kaynakça (16)

  1. H. Wilson and J. Cowan, “A Mathematical theory of the functional dynamics of cortical and thalamic nervous tissue”, Biological Cybernetics. vol. 13, no. 2, pp. 55-80, 1973.
  2. S. I. Amari, “Dynamics of pattern formation in lateral-inhibition type neural fields,” Biological Cybernetics. vol. 27, no. 2, pp. 77-87, 1977.
  3. S. Coombes, “Waves, bumps, and patterns in neural field theories,” Biological Cybernetics, vol. 93, no. 2, pp 91-108, 2005.
  4. S. Coombes, N.A. Venkov, L. Shiau, L. Bojak, D.T.J. Liley, C.R. Laing, “Modeling electrocortical activity through improved local approximations of integral neural field equations,” Phys. Rev. E 76, 051901, 2007.
  5. C. Huang and S. Vandewalle, “An analysis of delay dependent stability for ordinary and partial differential equations with fixed and distributed delays,” SIAM Journal on Scientific Computing, vol. 25, no. 5, pp.1608-1632, 2004.
  6. S. A. Van Gils, S. G. Janssens, Yu. A. Kuznetsov and S. Visser, “On local bifurcations in neural field models with transmission delays,” Journal of Mathematical Biology, vol. 66, no. 4, pp 837-887, 2013.
  7. R. Veltz, “Interplay between synaptic delays and propagation delays in neural field equations,” Siam Journal of Applied Dynamical Systems, vol. 12, no. 3, pp. 1566-1612, 2013.
  8. R. Veltz and O. Faugeras, “Stability of the stationary solutions of neural field equations with propagation delay,” Journal of Mathematical Neuroscience, 1,1,2011.
  9. R. Veltz and O. Faugeras, “A center manifold result for delayed neural fields equations,” Siam Journal on Mathematical Analysis, vol. 45, no. 3, pp. 1527-1562, 2013.
  10. G. Faye and O. Faugeras, “Some theoretical and numerical results for delayed neural field equations,” Physica D: Nonlinear Phenomena, vol. 239, no. 9, pp. 561-578, 2010.
  11. B. Özgür and A. Demir, “Some stability charts of a neural field model of two neural populations,” Communications in Mathematics and Applications, vol. 7, no. 2, 2016.
  12. B. Özgür, A. Demir and S. Erman, “A note on the stability of a neural field model,” Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 6, 2018.
  13. B. Özgür and A. Demir, “On the stability of two neuron populations interacting with each other,” Rocky Mountain Journal of Mathematics, vol. 48, no. 7, 2018.
  14. F. M. Atay and A. Hutt, “Stability and bifurcations in neural fields with finite propagation speed and general connectivity,” Siam Journal on Mathematical Analysis, vol. 5, no. 4, pp. 670-698, 2006.
  15. J. Forde and P. Nelson, “Applications of Sturm sequences to bifurcation analysis of delay differential equation models,” Journal of Mathematical Analysis and Applications, 300, pp. 273-284, 2004.
  16. R. Veltz and O. Faugeras, “Stability of the stationary solutions of neural field equations with propagation delay,” Journal of Mathematical Neuroscience, 1,1,2011.