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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,11]]},"abstract":"<jats:p> In this paper, fractional-order recurrent neural network models with Caputo Derivative are investigated. Firstly, we mainly focus our attention on Hopf bifurcation conditions for commensurate fractional-order network with time delay to reveal the essence that fractional-order equation can simulate the activity of neuron oscillation. Secondly, for incommensurate fractional-order neural network model, we prove the stability of the zero equilibrium point to show that incommensurate fractional-order neural network still converges to zero point. 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