Journal
NEURAL COMPUTATION
Volume 18, Issue 12, Pages 3009-3051Publisher
MIT PRESS
DOI: 10.1162/neco.2006.18.12.3009
Keywords
-
Ask authors/readers for more resources
A fundamental challenge for any general theory of neural circuits is how to characterize the structure of the space of all possible circuits over a given model neuron. As a first step in this direction, this letter begins a systematic study of the global parameter space structure of continuous-time recurrent neural networks (CTRNNs), a class of neural models that is simple but dynamically universal. First, we explicitly compute the local bifurcation manifolds of CTRNNs. We then visualize the structure of these manifolds in net input space for small circuits. These visualizations reveal a set of extremal saddle node bifurcation manifolds that divide CTRNN parameter space into regions of dynamics with different effective dimensionality. Next, we completely characterize the combinatorics and geometry of an asymptotically exact approximation to these regions for circuits of arbitrary size. Finally, we show how these regions can be used to calculate estimates of the probability of encountering different kinds of dynamics in CTRNN parameter space.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available