Computers perform poorly in comparison with the human brain for everyday tasks because they evolved from a 1940's number crunching architecture. New architectures are needed, more appropriate for current everyday tasks: web database search, network communication and recognition. For a new computer architecture, we consider the Wilson Cowan biological neural network (BNN) model of the brain which couples excitatory and inhibitory neurons in an additive neural model with sigmoid nonlinearity. We analyze the Wilson Cowan equations to demonstrate supercritical Hopf bifurcation that switches the neural oscillator between off and a stable oscillation---a basic operation in the brain. To mimic the Wilson Cowan neuron, we propose a novel all-optical artificial neural network (ANN) architecture in which semiconductor optical amplifiers (SOAs) perform addition and provide optical injection to a laser diode. We analyze the proposed all-optical system to show that it also performs supercritical Hopf bifurcation, although in this case with 3-D time trajectories rather than 2-D ones. We conclude that the all-optical system has as much dynamic capability as the mathematical brain model. This research aims to stimulate the development of physical analogs to the brain for future computing and better understanding of the brain.