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. 1990 Dec;87(23):9467–9471. doi: 10.1073/pnas.87.23.9467

Oscillations and chaos in neural networks: an exactly solvable model.

L P Wang 1, E E Pichler 1, J Ross 1
PMCID: PMC55187  PMID: 2251287

Abstract

We consider a randomly diluted higher-order network with noise, consisting of McCulloch-Pitts neurons that interact by Hebbian-type connections. For this model, exact dynamical equations are derived and solved for both parallel and random sequential updating algorithms. For parallel dynamics, we find a rich spectrum of different behaviors including static retrieving and oscillatory and chaotic phenomena in different parts of the parameter space. The bifurcation parameters include first- and second-order neuronal interaction coefficients and a rescaled noise level, which represents the combined effects of the random synaptic dilution, interference between stored patterns, and additional background noise. We show that a marked difference in terms of the occurrence of oscillations or chaos exists between neural networks with parallel and random sequential dynamics.

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Selected References

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