Equivalent Dynamics from Disparate Synaptic Weights in a Prevalent Visual Circuit

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 about a resonant frequency determined by the two effective synaptic parameters.