Chaotic Dynamics of High Order Neural Networks

The dynamics of an extremely diluted neural network with high order synapses acting as corrections to the Hopfield model is investigated. As in the fully connected case, the high order terms may strongly improve the storage capacity of the system. The dynamics displays a very rich behavior, and in particular a new chaotic phase emerges depending on the weight of the high order connections $\epsilon$, the noise level $T$ and the network load defined as the rate between the number of stored patterns and the mean connectivity per neuron $\alpha =P/C$.