Author | Heiden, Uwe an der. author |
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Title | Analysis of Neural Networks [electronic resource] / by Uwe an der Heiden |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1980 |
Connect to | http://dx.doi.org/10.1007/978-3-642-45517-9 |
Descript | X, 164 p. online resource |
1. The general form of a neural network -- 1.1 Introduction -- 1.2 The transformation of impulse frequencies into generator potentials (intercellular transmission) -- 1.3 The transformation of generator potentials into impulse frequencies (intracellular transmission) -- 1.4 Structures of neural networks -- 2. On the relations between several models for neural networks -- 2.1 The retinal network of Limulus polyphemus; the Hartline-Ratliff equations -- 2.2 A statistical approach: activities in coupled neuron pools; models of Cowan, Feldman, Wilson -- 2.3 Discrete models -- 3. Existence and uniqueness of time dependent solutions -- 4. Steady states of finite-dimensional networks -- 4.1 Existence problem -- 4.2 The number of steady states -- 4.3 Input-output behavior of stationary networks -- 4.4 An example of spatial hysteresis -- 5. Local stability analysis of nets with finitely many neurons -- 5.1 Introduction -- 5.2 The linearization principle -- 5.3 Some simple general criteria for asymptotic stability -- 5.4 Single neurons -- 5.5 Pairs of neurons -- 5.6 Closed chains of neurons -- 6. Oscillations in nets with finitely many neurons -- 6.1 Introduction -- 6.2 Oscillations in closed chains of neurons -- 6.3 Oscillations in systems with delays -- 7. Homogeneous tissues with lateral excitation or lateral inhibition -- 7.1 Introduction -- 7.2 The model -- 7.3 Stationary solutions and their stability -- 7.4 Thresholds in bistable tissues -- 7.5 Traveling fronts -- 7.6 Diverging pairs of fronts (spread of excitation or depression) -- 8. Homogeneous tissues with lateral excitation and self-inhibition -- 8.1 The model -- 8.2 Bulk oscillations -- 8.3 Traveling pulses (solitary waves) -- 8.4 Traveling wave trains -- 9. Homogeneous tissues with lateral inhibition and self- or local excitation -- 9.1 The model -- 9.2 Periodic spatial patterns -- 9.3 Stability -- 9.4 Miscellaneous topics -- References -- List of symbols