HOLDEN, ARUN V. “Structural, functional and dynamical hierarchies in neural networks.” In A chaotic hierarchy , pp. 187-197. 1991.
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Vertebrate neural systems have a modular, hierarchical anatomical structure, which is viewed as providing a hierarchical motor control or sensory analysis function. If each level in such a structural-functional hierarchy is considered as a dynamical system, its behaviour may be classified in a dynamical hierarchy, from equilibria, through periodicity, quasi-periodicity to chaos and higher order structured irregularities. These stuctural-functional and dynamical concepts of hierarchy may be combined if the spatio-temporal patterning of neural activity is considered. Spatio-temporal behaviour in a system which may be represented by a nonlinear partial differential system is often dominated by only a few degrees of freedom, and so may be approximated by nonlinear systems of low dimensionality. The nervous system is spatially extensive, but is a hierarchy of interacting subsystems. Each subsystem may be approximated by a nonlinear system of low dimensionality. Such a hierarchical network of coupled interacting subsystems generates a richness of patterned and irregular behaviours that is coherent over several levels and is determined by the network connectivity rather than the component and subsystem dynamics. The behaviour itself has a hierarchical structure, whose elements are not a simple mapping of the elements of the structural-functional or dynamical hierarchies …