Recurrent connections

I know that the first recurrent connection is to approximate the function in the realization graph

But I don’t understand what is the point of using circular join again.
Could you help me , thanks.

I agree, that example is written in a bit of a confusing manner. Where is it from?

When implementing a dynamical system dx/dt = f(x) in neurons, you need your “neural” feedback to be given by I + tau*f(x), where I is an identity matrix and tau is your recurrent synapse time constant. (A good example of this in action is the Lorenz attractor example.) So in your code, the nengo.Connection(a, a) is implementing the identity matrix portion of this equation. I think that code is also incorrect in that it uses dt in f(x) where it should use tau.