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dc.contributor.authorCohen, Michael A.en_US
dc.date.accessioned2011-11-14T18:23:38Z
dc.date.available2011-11-14T18:23:38Z
dc.date.issued1992-02en_US
dc.identifier.urihttps://hdl.handle.net/2144/2087
dc.description.abstractWe wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.en_US
dc.description.sponsorshipAir Force Office of Scientific Research (90-0128)en_US
dc.language.isoen_USen_US
dc.publisherBoston University Center for Adaptive Systems and Department of Cognitive and Neural Systemsen_US
dc.relation.ispartofseriesBU CAS/CNS Technical Reports;CAS/CNS-TR-1992-007en_US
dc.rightsCopyright 1992 Boston University. Permission to copy without fee all or part of this material is granted provided that: 1. The copies are not made or distributed for direct commercial advantage; 2. the report title, author, document number, and release date appear, and notice is given that copying is by permission of BOSTON UNIVERSITY TRUSTEES. To copy otherwise, or to republish, requires a fee and / or special permission.en_US
dc.titleThe Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universalityen_US
dc.typeTechnical Reporten_US
dc.rights.holderBoston University Trusteesen_US


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