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Consensus equation, help please.

  1. Nov 3, 2007 #1

    I am having the most trouble understanding this equation. Why is the limit of summation, declared as a node j in a member of the neighbors of agents i (Which is a set of nodes and links, taken from disk graphs)? Why is it that by the term [tex]x_j(t)[/tex], a derivative of X(of the i index) must be taken? Can anyone explain how this equation works?

    I am sure that this is a very difficult question and may take time to answer it, but I would heavily appriciate it if anyone can explain it well, as my research is at stake here.

    More information about this equation can be found on slide #11 of powerpoint presentation.

    http://www.piaggio.ccii.unipi.it/Bertinoro 2007/Materiale Didattico/EgerstedtTalk.pdf
  2. jcsd
  3. Nov 3, 2007 #2


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    If i=1, N1= {1} so [itex]\overdot{x}[/itex]1= x1- x1= 0.
    If i= 2, N2= {1, 2} so [itex]\overdot{x}[/itex]2= (x32- x1)+ (x2- x2= x2- x1
    If i= , N3= {1,2,3} so [itex]\overdot{x}[/itex]= (x3- x1)+ (x3)+ (x3- x2)+ x3- x1)= 2x3- x1-x2.
    Last edited: Nov 6, 2007
  4. Nov 3, 2007 #3
    Ok, I stared at what you said for 10 minutes but failed to understand it. Can you please provide additional details?
  5. Nov 5, 2007 #4
  6. Nov 7, 2007 #5
    :( anyone?
  7. Nov 11, 2007 #6
  8. Nov 11, 2007 #7


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    My non-technical understanding is that the change in node i is an average of the distances between i and its neighbors. So, if node i is agnostic in its beliefs, and its distance to node 1i (who is atheist) is x1i - xi = d1i, and its distance to node 2i (who is religious) is x2i - xi = d2i, then i's beliefs will change in proportion to the average distance to its neighbors: (d1i + d2i)/2. If i's initial distance to 1i is greater than its initial distance to 2i, d1i > d2i, then in the next period (or iteration) i's beliefs will get closer to 1i.
    Last edited: Nov 11, 2007
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