Generally, nerual netwoks can be descrbied by a ODE such as $\dot{x}=-Ax+Bf(x)+I$?
How is the ODE derived? What is the relation between the nerual netwoks model and nerual netwoks algorithms in computer science?
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maybe this wikipedia entry might help as a starting point :
http://en.wikipedia.org/wiki/Connectionism
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Thanky you, Fabrice Clerot.
http://www.scholarpedia.org/article/Hopfield_network#Computers_as_dynamical_systems
On this web, here are two popular forms of the model for Hopfield network:
Binary neurons with discrete time, updated one at a time
Vj(t+1)={1,0, if ΣkTjkVk(t)+Ij>0 otherwise
Graded neurons with continuous time
dxj/dt=−xj/τ+ΣkTjkg(xk)+Ij .
What is the relation between the two nerual netwoks models?
9th Sep, 2014
Fabrice Clerot
Orange Labs
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see :
http://www.scholarpedia.org/article/Hopfield_network#Graded_neuron_response_and_continuous_variables
the last lines of this entry gives you a relationship between the two models in a particular limit case (in general they are completely different) and even in this particular case where the minima are the same, the dynamics of the two networks is still different (as i vaguely remember, you should check that with more knowledgeable persons than me !)
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