Some Stability Charts of A Neural Field Model of Two Neural Populations

Authors

  • Berrak í–zgür Department of Mathematics, Faculty of Arts and Sciences, Kocaeli University, Umuttepe Campus, 41380, Kocaeli
  • Ali Demir Department of Mathematics, Faculty of Arts and Sciences, Kocaeli University, Umuttepe Campus, 41380, Kocaeli

DOI:

https://doi.org/10.26713/cma.v7i2.481

Abstract

In this paper, we study on the neural field model of two neuron populations. We make the stability analysis of the linearized model by considering the e¤ect of the synaptic connectivity function. We separate the plane into regions on which we find the number of roots with positive real parts. Hence we find the asymptotic stability region. To separate the plane we use the D-curves and we determine some properties of these curves.

Downloads

Download data is not yet available.

References

Amari, S.I., Dynamics of pattern formation in lateral-inhibition type

neural fields. Biol. Cybern. 27(2), 77-87 (1977)

Atay, F.M., Hutt, A., Stability and bifurcations in neural fields with finite propagation speed and general connectivity, Siam Journal on Mathematical Analysis 5(4), 670-698 (2006)

Coombes, S., Waves, bumps, and patterns in neural field theories, Bio-

logical Cybernetics, Volume 93, Issue 2, pp 91-108, (2005)

Coombes, S., Venkov, N.A., Shiau, L., Bojak, L., Liley, D.T.J., Laing,

C.R., Modeling electrocortical activity through improved local approximations

of integral neural field equations, Phys. Rev. E 76, 051901, (2007)

Faye, G., Faugeras, O., Some theoretical and numerical results for delayed

neural field equations, Physica D: Nonlinear Phenomena, Volume 239, Issue 9,

Pages 561-578, (2010)

Huang, C., Vandewalle, S., An analysis of delay dependent stability for

ordinary and partial di¤erential equations with fixed and distributed delays,

SIAM Journal on Scientific Computing, 25(5):1608-1632, (2004)

Insperger, T., Stépán, G., Semi-discretization for time-delay systems,

Stability and engineering applications, Springer New York, (2011)

Stépán, G., Retarded dynamical systems: stability and characteristic

functions, Longman Scientific & Technical, England, (1989)

Van Gils, S. A., Janssens, S. G., Kuznetsov, Yu. A., Visser, S., On

local bifurcations in neural field models with transmission delays, Journal of

Mathematical Biology, Volume 66, Issue 4, pp 837-887, (2013)

Veltz, R., Interplay between synaptic delays and propagation delays

in neural field equations. Siam Journal of Applied Dynamical Systems, 12(3),

-1612 (2013)

Veltz, R., Faugeras, O.,A center manifold result for delayed neural fields

equations, Siam Journal on Mathematical Analysis 45(3), 1527-1562 (2013)

Veltz, R., Faugeras, O., Stability of the stationary solutions of neural

field equations with propagation delay. Journal of Mathematical Neuroscience

:1 (2011)

Wilson, H., Cowan, J., A Mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Biol. Cybern. 13(2), 55-80 (1973)

Downloads

Published

09-11-2016
CITATION

How to Cite

í–zgür, B., & Demir, A. (2016). Some Stability Charts of A Neural Field Model of Two Neural Populations. Communications in Mathematics and Applications, 7(2), 159–166. https://doi.org/10.26713/cma.v7i2.481

Issue

Section

Research Article