Attractive Periodic Sets in Discrete-Time Recurrent Networks (with Emphasis on Fixed-Point Stability and Bifurcations in Two-Neuron Networks)

@article{Tio2001AttractivePS,
title={Attractive Periodic Sets in Discrete-Time Recurrent Networks (with Emphasis on Fixed-Point Stability and Bifurcations in Two-Neuron Networks)},
author={Peter Ti{\~n}o and Bill G. Horne and C. Lee Giles},
journal={Neural Computation},
year={2001},
volume={13},
pages={1379-1414}
}

We perform a detailed fixed-point analysis of two-unit recurrent neural networks with sigmoid-shaped transfer functions. Using geometrical arguments in the space of transfer function derivatives, we partition the network state-space into distinct regions corresponding to stability types of the fixed points. Unlike in the previous studies, we do not assume any special form of connectivity pattern between the neurons, and all free parameters are allowed to vary. We also prove that when both… CONTINUE READING