BE 539 Neural Networks, Chaos, and Dynamics:                       Theory and Application

Physiology and anatomy of living neurons and neural networks; Brain organization; Elements of nonlinear dynamics, the driven pendulum as paradigm for complexity, synchronicity, bifurcation, self-organization and chaos; Iterative maps on the interval, period-doubling route to chaos, universality and the Feigenbaum constant, Lyapunov exponents, entropy and information; Geometric characterization of attractors; Fractals and the Mandelbrot set; Neuron dynamics: from Hudgkin-Huxley to integrate and fire, bifurcation neuron; Artificial neural networks and connectionist models, Hopfield (attractor-type) networks,energy functions, convergence theorems, storage capacity, associative memory, pattern classification, pattern completion and error correction, the Morita network; Stochastic networks, simulated annealing and the Boltzmann machine, solution of optimization problems, hardware implementations of neural networks; the problem of learning, algorithmic approaches: Perception learning, back-propagation, Kohonnen's self-organizing maps and other networks; Coupled-map lattices; Selected applications including financial markets.

Department of Bioengineering
School of Engineering and Applied Science
University of Pennsylvania
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