  Stylized models of the neurodynamics that underpin sensory motor control in
animals are proposed and studied. The voluntary motions of animals are
typically initiated by high level intentions created in the primary cortex
through a combination of perceptions of the current state of the environment
along with memories of past reactions to similar states. Muscle movements are
produced as a result of neural processes in which the parallel activity of
large multiplicities of neurons generate signals that collectively lead to
desired actions. Essential to coordinated muscle movement are intentionality,
prediction, regions of the cortex dealing with misperceptions of sensory cues,
and a significant level of resilience with respect to disruptions in the neural
pathways through which signals must propagate. While linear models of feedback
control systems have been well studied over decades, this paper proposes and
analyzes a class of models whose aims are to capture some of the essential
features of neural control of movement. Whereas most linear models of feedback
systems entail a state component whose dimension is higher than the number of
inputs or outputs, the work that follows will treat models in which the numbers
of input and output channels greatly exceed the state dimension. While we begin
by considering continuous time systems, the aim will be to treat systems whose
evolution involves classes of inputs that emulate neural spike trains. Within
the proposed class of models, the paper will study resilience to channel
dropouts, the ways in which noise and uncertainty can be mitigated by an
appropriate notion of consensus among noisy inputs, and finally, by a simple
model in which binary activations of a multiplicity of input channels produce a
dynamic response that closely approximates the dynamics of a prescribed linear
system whose inputs are continuous functions of time.
