Analysis of Neural Networks
Alan G. Hawkes, Uwe an der Heiden · Biometrics · 1982
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.- a) the logical neurons of McCulloch and Pitts.- b) discrete time and continuous states.- 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.- a) single neurons.- b) pairs of neurons.- c) arbitrarily many neurons.- 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.