Time-Oriented Synthesis for a WTA Continuous-Time Neural Network Affected by Capacitive Cross-Coupling

A continuous time neural network built with nonlinear amplifiers which selects the largest item of a list (WTA) is considered. The network receives and processes lists admitted one by one. If the processing and resetting times are imposed, our paper gives a method to find the circuit parameters assuring a correct operation. We take into account the capacitive coupling between input terminals and present complete existence and convergence results on the differential model. The main achievement consists of simple bounds for the processing and resetting times. They are inferred by an original method of decoupling the system model into solvable linear differential inequalities. Also, a new procedure to impose the stationary WTA state is given. All these results are valid under various parameter restrictions. They lead to a neat design procedure which starts from imposed processing and resetting time and list density to determine the WTA threshold, the interconnection conductance, the amplifier gain, the bias current. Numerical examples check and interpret the results.