## Analysis of neural networks |

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### Contents

The general form of a neural network | 1 |

0n the relations between several models for neural networks | 14 |

Existence and uniqueness of time dependent solutions | 21 |

Copyright | |

6 other sections not shown

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0bviously amplitude Assume asymptotically stable axon axon hillock behavior bounded function cell chapter characteristic equation constant solution continuous function convex set corresponding Cowan decreasing defined delays denotes derived determined differential equation eigenvalue exactly one solution experimental Fife finite fixed point function f Hadeler hysteresis phenomena implies impulse frequency inequality inhibitory initial condition integral equations interaction interval investigated lateral excitation lateral inhibition lemma mathematical matrix membrane potential monotone increasing Moreover neural networks neurons non-constant nonnegative obeying obtained oscillations periodic solution perturbations positive real potential proof pulse respect right hand side Rinzel and Keller root satisfying self-inhibition sigmoid function single neuron solution of 7.7 solution v(s,t spectral radius spike stationary solutions steady synapses temporal weight function theorem 5.2 theory threshold tissue traveling front traveling wave unique unstable variables vector wave train weight functions