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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Undamped Oscillations Generated by Hopf Bifurcations in Fractional-Order Recurrent Neural Networks With Caputo Derivative
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Undamped Oscillations Generated by Hopf Bifurcations in Fractional-Order Recurrent Neural Networks With Caputo Derivative

机译：具有Caputo导数的分数阶递归神经网络中Hopf分叉产生的无阻尼振荡

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摘要

In this paper, a fractional-order recurrent neural network is proposed and several topics related to the dynamics of such a network are investigated, such as the stability, Hopf bifurcations, and undamped oscillations. The stability domain of the trivial steady state is completely characterized with respect to network parameters and orders of the commensurate-order neural network. Based on the stability analysis, the critical values of the fractional order are identified, where Hopf bifurcations occur and a family of oscillations bifurcate from the trivial steady state. Then, the parametric range of undamped oscillations is also estimated and the frequency and amplitude of oscillations are determined analytically and numerically for such commensurate-order networks. Meanwhile, it is shown that the incommensurate-order neural network can also exhibit a Hopf bifurcation as the network parameter passes through a critical value which can be determined exactly. The frequency and amplitude of bifurcated oscillations are determined.
机译：在本文中，提出了分数阶递归神经网络，并研究了与该网络的动力学相关的几个主题，例如稳定性，Hopf分叉和无阻尼振荡。相对于网络参数和相序神经网络的阶数，微不足道的稳定状态的稳定性域得到了完全表征。基于稳定性分析，确定分数阶的临界值，在该处出现Hopf分叉，并且从平凡稳态开始出现一族振荡。然后，还估计了无阻尼振荡的参数范围，并通过解析和数字方式确定了此类同阶网络的振荡频率和幅度。同时表明，当网络参数通过可以精确确定的临界值时，不等阶神经网络也可能表现出霍普夫分支。确定分叉振荡的频率和幅度。

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