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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.
L P Wang, and
E E Pichler, and
J Ross
September 2013,
Chaos (Woodbury, N.Y.),
L P Wang, and
E E Pichler, and
J Ross
January 2012,
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L P Wang, and
E E Pichler, and
J Ross
July 2013,
Physical review letters,
L P Wang, and
E E Pichler, and
J Ross
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L P Wang, and
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L P Wang, and
E E Pichler, and
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L P Wang, and
E E Pichler, and
J Ross
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L P Wang, and
E E Pichler, and
J Ross
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L P Wang, and
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J Ross
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L P Wang, and
E E Pichler, and
J Ross
June 1999,
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