## Analysis of Dynamical and Cognitive Systems: Advanced Course, Stockholm, Sweden, August 9 - 14, 1993. ProceedingsThis volume constitutes the documentation of the advanced course on Analysis of Dynamical and Cognitive Systems, held during the Summer University of Southern Stockholm in Stockholm, Sweden in August 1993. The volume contains eight carefully revised full versions of the invited three-to-four hour presentations as well as two abstracts. As a consequence of the interdisciplinary topic, several aspects of dynamical and cognitive systems are addressed: there are three papers on computability and undecidability, five tutorials on diverse aspects of universal cellular neural networks, and two presentations on dynamical systems and complexity. |

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### Contents

The Limits of Mathematics Course Outline and Software | 1 |

Historical Background of Godels Theorem | 3 |

A Formal Scheme for Avoiding Undecidable Problems Applications to Chaotic Behavior Characterization and Parallel Computation | 9 |

Cellular Neural Networks A Tutorial on Programmable Nonlinear Dynamics in Space | 53 |

A Theoretical Vista of Mechanisms Techniques and Applications | 75 |

Hebbian Unlearning | 121 |

Mapping Discounted and Undiscounted Markov Decision Problems onto Hopfield Neural Networks | 137 |

A modelbased and an inductive approach | 169 |

Simplicity criteria for dynamical systems | 189 |

Attraction and Composition | 227 |

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accepting automaton algorithm alphabet application attraction attractor automata axiom behaviour blobs bounded limits cell Cellular Neural Networks chaotic dynamics chaotic limits chaotic systems coding complex computation computer vision consider convergence cycle Decision Problems defined definition denote domain dyadic map dynamical systems equation eventually periodic exists factor feature vector Figure finite automaton fixed point formal full and atomic gamma camera Hebbian Hebbian learning Hemmen Hopfield Hopfield network infinite input integer interval invariant inverse iteration labeling language Lemma Lyapunov function maximal natural numbers neural networks neurons nonempty nonlinear obtain operation optimal oscillations overlap patterns Peano's axioms perceptron periodic points predicate transformers procedure processing programs projector matrix Proof properties Proposition recursive functions regular Scenario segmentation self-interaction sequence space spike stationary steps stimulus strategy subshift symbolic dynamics synaptic synchronous template Theorem theory topologically transitive undecidability undiscounted unimodal systems unlearning value-iteration

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Page 260 - Stability of Fixed Points and Periodic Orbits and Bifurcations in Analog Neural Networks,