School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China.
School of Mathematics, and Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing 210996, China; School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, China.
Neural Netw. 2018 Feb;98:223-235. doi: 10.1016/j.neunet.2017.11.020. Epub 2017 Dec 6.
The effects of leakage delay on the dynamics of neural networks with integer-order have lately been received considerable attention. It has been confirmed that fractional neural networks more appropriately uncover the dynamical properties of neural networks, but the results of fractional neural networks with leakage delay are relatively few. This paper primarily concentrates on the issue of bifurcation for high-order fractional bidirectional associative memory(BAM) neural networks involving leakage delay. The first attempt is made to tackle the stability and bifurcation of high-order fractional BAM neural networks with time delay in leakage terms in this paper. The conditions for the appearance of bifurcation for the proposed systems with leakage delay are firstly established by adopting time delay as a bifurcation parameter. Then, the bifurcation criteria of such system without leakage delay are successfully acquired. Comparative analysis wondrously detects that the stability performance of the proposed high-order fractional neural networks is critically weakened by leakage delay, they cannot be overlooked. Numerical examples are ultimately exhibited to attest the efficiency of the theoretical results.
最近，人们对具有整数阶的神经网络的泄漏延迟对动力学的影响给予了相当的关注。已经证实，分数阶神经网络更能揭示神经网络的动力学特性，但是具有泄漏延迟的分数阶神经网络的结果相对较少。本文主要关注涉及泄漏延迟的高阶分数阶双向联想记忆（BAM）神经网络的分岔问题。本文首次尝试解决具有泄漏延迟的高阶分数阶 BAM 神经网络的稳定性和分岔问题。首先，通过采用时滞作为分岔参数，建立了具有泄漏延迟的所提出系统出现分岔的条件。然后，成功获得了没有泄漏延迟的此类系统的分岔准则。比较分析惊人地发现，泄漏延迟极大地削弱了所提出的高阶分数阶神经网络的稳定性性能，它们不能被忽视。最后，给出了数值例子来证明理论结果的有效性。
