Answers.Body: <p>I think that the book "Neural Networks and Learning Machines" of Haykin can help you. In his book the chapter 13 is about neural dynamics, and there are some examples of how analise the dynamics of network.</p>
  
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Answers.CreationDate: 2020-04-18T20:35:53.963Z
Answers.Text: This is a very comprehensive book. I read the chapter "Neurodynamics". Some old questions were gone, but new ones appeared instead. In general, I feel that this material needs to be started. Thank you for the answer, I will think about how to adapt it to my tasks.
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Body: <p>Neural networks with feedback (Hopfield, Hamming, etc.) differ from ordinary neural networks (multilayer perceptrons, etc.), which turns them into a dynamic element with its own internal dynamics (if we consider them as a separate dynamic link). The following question naturally arises - is it possible to represent them in the form of state spaces? </p>
  
  <p>Nuance is that feedback is created by introducing a delay element, which means recording a neural network exclusively in a discrete form. Is continuous recording possible? What acts as matrices A, B, C, D? How does the presence of nonlinear activation functions affect?
  The only more or less useful information that I managed to find is in this article:</p>
  
  <p><a href="https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930021849.pdf" rel="nofollow noreferrer">On neural networks in identification and control of dynamic systems. 3.2 Paragraph. Page 8</a></p>
  
  <p>But my assumptions are only confirmed there, which does not clarify the situation.</p>
  
  <p>In general, if someone has come across this and can assist in studying the issue, please share links, possibly examples, etc.</p>
  
Tags: <recurrent-neural-networks><models><control-problem>
Title: Neural networks with internal dynamics in the state-space form
UserDisplayName: ayr
ThreadText: # Neural networks with internal dynamics in the state-space form
  
  (Asked by: username_0 on 2020-04-18)
  
  Neural networks with feedback (Hopfield, Hamming, etc.) differ from ordinary neural networks (multilayer perceptrons, etc.), which turns them into a dynamic element with its own internal dynamics (if we consider them as a separate dynamic link). The following question naturally arises - is it possible to represent them in the form of state spaces?
  
  Nuance is that feedback is created by introducing a delay element, which means recording a neural network exclusively in a discrete form. Is continuous recording possible? What acts as matrices A, B, C, D? How does the presence of nonlinear activation functions affect?
  The only more or less useful information that I managed to find is in this article:
  
  [On neural networks in identification and control of dynamic systems. 3.2 Paragraph. Page 8](https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930021849.pdf)
  
  But my assumptions are only confirmed there, which does not clarify the situation.
  
  In general, if someone has come across this and can assist in studying the issue, please share links, possibly examples, etc.
  
  **Tags:** recurrent-neural-networks, models, control-problem
  
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  ## 1 answers
  
  ### Answer by username_1 on 2020-04-18. Score: 1 | Accepted answer
  
  I think that the book "Neural Networks and Learning Machines" of Haykin can help you. In his book the chapter 13 is about neural dynamics, and there are some examples of how analise the dynamics of network.
  
  > **Comments:**
  > **username_0**: This is a very comprehensive book. I read the chapter "Neurodynamics". Some old questions were gone, but new ones appeared instead. In general, I feel that this material needs to be started. Thank you for the answer, I will think about how to adapt it to my tasks.  
  
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