A brain can perform pattern recognition tasks that are not yet
possible for an electronic computer. We continue here our
investigation of electronic circuits that are inspired by knowledge
of structures in a brain. These circuits are oscillators that are
motivated by principles of neuroscience, but yet are constructible
as micro circuits, and possibly as nano-circuits. Populations of
such oscillators can exhibit patterns in their output frequencies.
This may be in response to an external signal being applied across
the population or in response to internal waves that propagate
through the population. We have investigated the former phenomenon
where coalitions of oscillators, classified by their output
frequency, form in response to a common driving signal. The
resulting patterns have been used to characterize the input signal
and they serve as a basis for comparison of signals and other
pattern recognition tasks. In this paper, we investigate pattern
formation that results from the propagation of synchronized activity
waves within the population of oscillators. The novelty here is in
the model: We derive a nonlinear wave equation to describe networks
of oscillators, and simulate solutions to demonstrate some basic
results.