The "brain-state-in-box" sounds like we have a brain in a box without body.  But the model is defined as follows:

Let W be a symmetric weight matrix whose largest eigenvalues have positive real components.  In addition, W is required to be positive semi-definite, i.e.,  xTWx >= 0 for all x.  Let x(0) denotes the initial state vector.  The BSB algorithm is defined by the pair of equations:

        y(n) = x(n) + h Wx(n),

        x(n+1) = f(y(n)).

Or more concisely, the updating rule of the "brain state" x (a vector) is

        x  <-  f(x + h W x)

where h is a small positive constant called the feedback factor.  The f is a piecewise-linear function of the form

        f(x) = +1     if x > 1;

        f(x) = x     if  -1 < x < 1;

        f(x) = -1     if x < -1.

When the W is choosing with the required property (positivity of largest eigenvalues), the effect of the algorithm is to drive the system for components of x to binary values +1 or 1 for each of the neuron.   We can view it as a mapping from continuous inputs x(0) to discrete binary outputs.  The final states are of the form (-1,+1,-1,-1,+1,+1, ..., +1).  This represents a corner of cube in an N-dimensional space of linear size 2, centered at origin.  This is the box of the brain-state-in "a box".   The dynamics is such that the state moves to the wall of the box and then drives to the corner of the box.

Application of BSB model

What is a good use of BSB model?  A natural application for the BSB model is clustering.  Such as the classification of radar signals from the source of emitters.  The matrix W has to be (unsupervised) learned using some of the methods discussed in early chapters.