Loading...
Search for:
neural-fields
0.004 seconds
Dynamics of Neural Fields Models With Delay
, M.Sc. Thesis Sharif University of Technology ; Fotuhi Firoozabad, Morteza (Supervisor)
Abstract
Neural field models with delays define a useful framework for modeling macroscopic parts of the cortex involving several populations of neurons. Nonlinear delayed integrodi fferential equations describe the spatio-temporal behavior of these fields. We also present a study of the numerical computation of these solutions in a special case. Another original contribution of ours is the definition of a Lyapunov functional and the result of stability it implies. We illustrate our work on a variety of examples that are relevant to modeling in neuroscience.
Continuous neural network with windowed Hebbian learning
, Article Biological Cybernetics ; Volume 109, Issue 3 , June , 2015 , Pages 321-332 ; 03401200 (ISSN) ; Heidari, M ; Sharifitabar, M ; Sharif University of Technology
Springer Verlag
2015
Abstract
We introduce an extension of the classical neural field equation where the dynamics of the synaptic kernel satisfies the standard Hebbian type of learning (synaptic plasticity). Here, a continuous network in which changes in the weight kernel occurs in a specified time window is considered. A novelty of this model is that it admits synaptic weight decrease as well as the usual weight increase resulting from correlated activity. The resulting equation leads to a delay-type rate model for which the existence and stability of solutions such as the rest state, bumps, and traveling fronts are investigated. Some relations between the length of the time window and the bump width is derived. In...
The Existence and Stability of Classical Solutions in the Neural Fields Equations
, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabadi, Morteza (Supervisor)
Abstract
In this thesis, first, the modeling method of neural fields is precisely presented. Then, Existence and Stability of different solutions of one dimensional neural fields like Standing Pulses, Traveling Waves and ... are investigated in three different models of neural fields. In order for proving Existence and Stability of the solutions the mathematical tools like Fourier transform and Evans function are applied. All the models which analysed in this thesis have the following Integro-Differential Equation form:
τ
∂u(x, t)
∂t
= −u(x, t) +
∫ +∞
−∞
w(x, y)f[u(y, t)]dy + I(x, t) + s(x, t)
and also in some models the parameters might be changed
τ
∂u(x, t)
∂t
= −u(x, t) +
∫ +∞
−∞
w(x, y)f[u(y, t)]dy + I(x, t) + s(x, t)
and also in some models the parameters might be changed
Neural fields with fast learning dynamic kernel
, Article Biological Cybernetics ; Volume 106, Issue 1 , January , 2012 , Pages 15-26 ; 03401200 (ISSN) ; Fotouhi, M ; Heidari, M ; Sharif University of Technology
Abstract
We introduce a modified-firing-rate model based on Hebbian-type changing synaptic connections. The existence and stability of solutions such as rest state, bumps, and traveling waves are shown for this type of model. Three types of kernels, namely exponential, Mexican hat, and periodic synaptic connections, are considered. In the former two cases, the existence of a rest state solution is proved and the conditions for their stability are found. Bump solutions are shown for two kinds of synaptic kernels, and their stability is investigated by constructing a corresponding Evans function that holds for a specific range of values of the kernel coefficient strength (KCS). Applying a similar...