  Neural feedback-triads consisting of two feedback loops with a non-reciprocal
lateral connection from one loop to the other are ubiquitous in the brain. We
show analytically that the dynamics of this network topology are determined by
two algebraic combinations of its five synaptic weights. Thus different weight
settings can generate equivalent network dynamics. Exploration of network
activity over the two-dimensional parameter space demonstrates the importance
of the non-reciprocal lateral connection and reveals intricate behavior
involving continuous transitions between qualitatively different activity
states. In addition, we show that the response to periodic inputs is narrowly
tuned around a center frequency determined by the two effective synaptic
parameters.
