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. The learning rules for the high-order connections contain mixing of memories, different from all the previous generalizations of the Hopfield model. The dynamics may display fixed points or periodic and chaotic orbits, depending on the weight of the high-order connections ε, the noise levelT, and the network load, defined as the ratio between the number of stored patterns and the mean connectivity per neuron, α=P/C. As in the related fully connected case, there is an optimal value of the weight ε that improves the storage capacity of the system (the capacity diverges).