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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 $alpha =P/C$.
We explore the influence of precision of the data and the algorithm for the simulation of chaotic dynamics by neural networks techniques. For this purpose, we simulate the Lorenz system with different precisions using three different neural network t
Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish, based on a r
We study the quantum chaotic dynamics of an initially well-localized wave packet in a cosine potential perturbed by an external time-dependent force. For our choice of initial condition and with $hbar$ small but finite, we find that the wave packet b
We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some textit{finite} precision, we propose a model where spikes
We study adaptive learning in a typical p-player game. The payoffs of the games are randomly generated and then held fixed. The strategies of the players evolve through time as the players learn. The trajectories in the strategy space display a range