  In neural information processing, an input modulates neural dynamics to
generate a desired output.
  To unravel the dynamics and underlying neural connectivity enabling such
input-output association, we proposed an exactly soluble neural-network model
with a connectivity matrix explicitly consisting of inputs and required
outputs.
  An analytic form of the response upon the input is derived, whereas three
distinctive types of responses including chaotic dynamics as bifurcation
against input strength are obtained depending on the neural sensitivity and
number of inputs.
  Optimal performance is achieved at the onset of chaos, and the relevance of
the results to cognitive dynamics is discussed.
