It is shown that the characteristic equation has roots with positive real part, when the physiological parameters have reasonable magnitudes. The significance of this fact is discussed.doi:10.1016/S0006-3495(79)85216-9A MuirElsevier Inc.Biophysical Journal...
Hutt A, Longtin A, Schimansky-Geier L (2008) Additive noise-induced turing transitions in spatial systems with application to neural fields and the swift-hohenberg equation. Phys D Nonlinear Phenom 237(6):755–773 Google Scholar Kilpatrick ZP, Bressloff PC (2010) Effects of synaptic depressio...
The Wilson-Cowan model describes the evolution of excitatory and inhibitory activity in a synaptically coupled neuronal network. As opposed to being a detailed biophysical model, the system is a coarse-grained description of the overall activity of a large-scale neuronal network, employing just two ...
and Haken discussed a theory comprising the brain wave equation proposed by Nunez, the Wilson–Cowan/Ermentrout–Cowan model, and Ho... TD Frank,A Daffertshofer,CE Peper,... - 《Physica D-nonlinear Phenomena》 被引量: 176发表: 2000年 Recognition of abstract objects via neural oscillators: ...
Then, by the properties of roots of the characteristic equation, normal form theory and center manifold Acknowledgments This research is partially sponsored by Natural Science Foundation of China-pl2X-sim-(Nos. 61572004, 61370113, 61672070, and 61650201), Beijing Municipal Natural Science Foundation (...
stochastic differential equationWilson–Cowan modelmean fieldspropagation of chaoselectrical synapsenonlinear coupling termIn this paper we prove the propagation of chaos property for an ensemble of interacting neurons subject to independent Brownian noise. The propagation of chaos property means that in the...
Wilson-Cowan modelweakly nonlocal limitWavelet-Galerkin methodWe derive the weakly nonlocal limit of a one - population neuronal field model of the Wilson - Cowan type in one spatial dimension. By transforming this equation to an equation in the firing rate variable, it is shown that stationary...
The solutions of the full nonlocal equation obey a uniform bound, and the stationary periodic solutions in the weakly nonlocal limit satisfying the same uniform bound are characterized by finite ranges of pseudo energy constants. The time dependent version of the model is reformulated as a ...
The solutions of the full nonlocal equation obey a uniform bound, and the stationary periodic solutions in the weakly nonlocal limit satisfying the same uniform bound are characterized by finite ranges of pseudo energy constants. Based on the shape of pseudopotential we also conjecture that the ...
The investigation is done through the examination of the\nsystem's associated characteristic equation. Under mild assumptions, we give\ncomplete mathematical proofs of our theoretical results, for the model with\ngeneral delay distributions and prove the transversality condition for the\npossible Hopf ...