Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression

Details Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression

2010-03-05

arxiv.org/abs/1003.1196v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

26 pages, 13 figures. Preliminary results for the present work have been published elsewhere (Y Igarashi et al., 2009. http:

Scientific paper

We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing state variable and a synaptic variable. In these equations, their average product is decoupled as the product of averaged them because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady state equations for a network with uniform connections and a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady state solutions. An oscillatory uniform state was observed in the network with uniform connections due to a Hopf instability. With the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previous unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.

Affiliated with

Also associated with

No associations

Rating

Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-687048