Retrieval and chaos in extremely diluted non-monotonic neural networks
M. S. Mainieri, R. Erichsen · 2002
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 Models of neural networks have been largely studied since the pioneering work of Hopfield [1]. Assuming symmetric interactions and monotonic units, and using classical tools of statistical mechanics, equilibrium properties were extensively investigated. For a review in this subject, see, e. g., [2]. Nevertheless,