Attractive periodic sets in discrete-time recurrent networks (with emphasis on fixed-point stability and bifurcations in two-neuron networks)

Peter Tiňo, Bill G. Horne, C. Lee Giles

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

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 neurons have excitatory self-connections and the mutual interaction pattern is the same (i.e., the neurons mutually inhibit or excite themselves), new attractive fixed points are created through the saddle-node bifurcation. Finally, for an N-neuron recurrent network, we give lower bounds on the rate of convergence of attractive periodic points toward the saturation values of neuron activations, as the absolute values of connection weights grow.

Original languageEnglish (US)
Pages (from-to)1379-1414
Number of pages36
JournalNeural Computation
Volume13
Issue number6
DOIs
StatePublished - Jun 1 2001

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Neurons
Sigmoid Colon
Neuron
Fixed Point
Weights and Measures

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience

Cite this

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Attractive periodic sets in discrete-time recurrent networks (with emphasis on fixed-point stability and bifurcations in two-neuron networks). / Tiňo, Peter; Horne, Bill G.; Giles, C. Lee.

In: Neural Computation, Vol. 13, No. 6, 01.06.2001, p. 1379-1414.

Research output: Contribution to journalArticle

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