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Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 6

A note on the stability of a neural field model

Berrak ÖZGÜR
Sertaç ERMAN
Ali DEMİR
Pages
1495–1502
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Moreover we study on the stability cases by considering the real roots of the characteristic equation.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper we consider the neural field model for two neural populations.
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Key Findings & Data:We investigate the properties of D-curves and we give some conditions for asymptotic stability.
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Conclusion & Impact:Moreover we study on the stability cases by considering the real roots of the characteristic equation.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Neural field model · asymptotic stability

Abstract

In this paper we consider the neural field model for two neural populations. We investigate the properties of D-curves and we give some conditions for asymptotic stability. The asymptotic stability region is determined by using the Stépan's formula. Taking various delay terms into account, the effect of delay on the stability is investigated. Moreover we study on the stability cases by considering the real roots of the characteristic equation.

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Cite This Article

ÖZGÜR, B., ERMAN, S., DEMİR, A. (2022). A note on the stability of a neural field model. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 6, 1495–1502. https://ajindex.com/articles/529835

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References (10)

  1. Amari, SI. Dynamics of pattern formation in lateral-inhibition type neural fields, Biol. Cybern. 27 (2), 77-87, 1977.
  2. Erman, S., Demir, A. An analysis on the stability of a state dependent delay differential equation, Open Math., 14 (1), 425-435,2016. Faye G. Symmetry breaking and pattern formation in some neural field equations, PhD thesis, University of Nice- Sophia Antipolis, 2012.
  3. Faye, G., Faugeras, O. Some theoretical and numerical results for delayed neural field equations, Physica D, 239 (9), 561-578, 2010.
  4. Huang, C., Vandewalle, S. An analysis of delay dependent stability for ordinary and partial differential equations with fixed and distributed delays, SIAM J. Sci. Comput., 25 (5), 1608-1632, 2004.
  5. Insperger, T., St\'{e}p\'{a}n, G. Semi-discretization for time-delay systems, Stability and engineering applications, New York, Springer, 2011.
  6. McCormick, DA., Connors, BW., Lighthall, JW., Prince, DA. Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex, J Neurophysiol, 54 (4), 782-806, 1985. Stépan, G. Retarded dynamical systems: stability and characteristic functions, England, Longman Scientific \& Technical, 1989.
  7. Veltz, R. Interplay between synaptic delays and propagation delays in neural field equations. Siam J Appl Dyn Syst, 12 (3), 1566-1612, 2013.
  8. Veltz, R., Faugeras, O. Stability of the stationary solutions of neural field equations with propagation delay. Journal of Mathematical Neuroscience 1:1, 2011.
  9. Veltz, R., Faugeras, O. A center manifold result for delayed neural fields equations, Siam J Math Anal 45 (3), 1527-1562, 2013.
  10. Wilson, H., Cowan, J. A Mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Biol. Cybern. 13 (2), 55-80, 1973.