Retrieval and Chaos in Extremely Diluted Non-Monotonic Neural Networks

Details Retrieval and Chaos in Extremely Diluted Non-Monotonic Neural Networks Retrieval and Chaos in Extremely Diluted Non-Monotonic Neural Networks

2002-02-06

arxiv.org/abs/cond-mat/0202097v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages, 4 figures

Scientific paper

10.1016/S0378-4371(02)00626-X

We discuss, in this paper, the dynamical properties of extremely diluted, non-monotonic neural networks. Assuming parallel updating and the Hebb prescription for the synaptic connections, a flow equation for the macroscopic overlap is derived. A rich dynamical phase diagram was obtained, showing a stable retrieval phase, as well as a cycle two and chaotic behavior. Numerical simulations were performed, showing good agreement with analytical results. Furthermore, the simulations give an additional insight into the microscopic dynamical behavior during the chaotic phase. It is shown that the freezing of individual neuron states is related to the structure of chaotic attractors.

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