Ivancevic_Applied-Diff-Geom

Applied Bundle Geometry 587Fig. 4.9 Sample output from the Human Biodynamics Engine: running with thespeed of 5 m/s.4.9.6.5 Open Liouville Neurodynamics and Biodynamical Self–SimilarityRecall (see [Ivancevic and Ivancevic (2006)]) that neurodynamics has itsphysical behavior both at the macroscopic, classical, inter–neuronal level,and at the microscopic, quantum, intra–neuronal level. At the macroscopiclevel, various models of neural networks (NNs, for short) have been proposedas goal–oriented models of the specific neural functions, like for instance,function–approximation, pattern–recognition, classification, or control(see, e.g., [Haykin (1994)]). In the physically–based, Hopfield–typemodels of NNs [Hopfield (1982); Hopfield (1984)] the information is storedas a content–addressable memory in which synaptic strengths are modifiedafter the Hebbian rule (see [Hebb (1949)]. Its retrieval is made when thenetwork with the symmetric couplings works as the point–attractor withthe fixed points. Analysis of both activation and learning dynamics ofHopfield–Hebbian NNs using the techniques of statistical mechanics [Domanyet al. (1991)], gives us with the most important information of storagecapacity, role of noise and recall performance.On the other hand, at the general microscopic intra–cellular level, en-