Abstract
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.
