# Homework Help: Consensus equation, help please.

1. Nov 3, 2007

### l46kok

http://img112.imageshack.us/img112/2433/consensusequationdv9.jpg [Broken]

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 $$x_j(t)$$, 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.

http://www.piaggio.ccii.unipi.it/Bertinoro%202007/Materiale%20Didattico/EgerstedtTalk.pdf [Broken]

Last edited by a moderator: May 3, 2017
2. Nov 3, 2007

### HallsofIvy

If i=1, N1= {1} so $\overdot{x}$1= x1- x1= 0.
If i= 2, N2= {1, 2} so $\overdot{x}$2= (x32- x1)+ (x2- x2= x2- x1
If i= , N3= {1,2,3} so $\overdot{x}$= (x3- x1)+ (x3)+ (x3- x2)+ x3- x1)= 2x3- x1-x2.
etc.

Last edited by a moderator: Nov 6, 2007
3. Nov 3, 2007

### l46kok

Ok, I stared at what you said for 10 minutes but failed to understand it. Can you please provide additional details?

4. Nov 5, 2007

anyone?

5. Nov 7, 2007

### l46kok

:( anyone?

6. Nov 11, 2007

### l46kok

7. Nov 11, 2007

### EnumaElish

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 by a moderator: May 3, 2017