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Chaotic Behavior of A Neural Network with Dynamical Thresholds

Models of neural networks which include dynamical thresholds can display motion in pattern space, the space of all memories. We investigate this motion in a particular model which is based on a feedback network of excitatory and inhibitory neurons. We find that small variations in the parameters of the model can lead to big qualitative changes of its behavior. We display results of closed loops and chaotic motion which turn from one to the other through intermittency. We show that the basin of attraction of a closed orbit has a fractal shape, and find that the dimension of the chaotic motion is slightly bigger than 2. The general character of the dynamics of this model is convergence to centers of attraction on short time scales and divergence on long ones.