We study a generalization of the brain-state-in-a-box (BSB) model for a class of nonlinear discrete dynamical systems where we allow the states of the system to lie in an arbitrary convex body. The states of the classical BSB model are restricted to lie in a hypercube. Characterizations of equilibrium points of the system are given using the support function of a convex body. Also, sufficient conditions for a point to be a stable equilibrium point are investigated. Finally, we study the system in polytopes. The results in this special case are more precise and have simpler forms than the corresponding results for general convex bodies. The general results give one approach of allowing pixels in image reconstruction to assume more than two values
S. Hui and M. Bohner, "Brain State in a Convex Body," IEEE Transactions on Neural Networks, Institute of Electrical and Electronics Engineers (IEEE), Jan 1995.
The definitive version is available at http://dx.doi.org/10.1109/72.410350
Mathematics and Statistics
Keywords and Phrases
Brain-State-In-A-Box Model; Content-Addressable Storage; Convex Body; Equilibrium Points; Generalisation (Artificial Intelligence); Generalization; Hypercube; Hypercube Networks; Image Reconstruction; Neural Model; Neural Nets; Nonlinear Discrete Dynamical Systems; Nonlinear Dynamical Systems; Polytopes; Sufficient Conditions
International Standard Serial Number (ISSN)
Article - Journal
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