Huang Chengdai, Wang Juan, Chen Xiaoping, Cao Jinde
School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China.
School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China.
Neural Netw. 2021 Sep;141:344-354. doi: 10.1016/j.neunet.2021.04.005. Epub 2021 Apr 18.
This paper illuminates the issue of bifurcations for a fractional-order bidirectional associative memory neural network(FOBAMNN) with four different delays. On account of the affirmatory presumption, the developed FOBAMNN is firstly transformed into the one with two nonidentical delays. Then the critical values of Hopf bifurcations with respect to disparate delays are calculated quantitatively by establishing one delay and selecting remaining delay as a bifurcation parameter in the transformed model. It detects that the stability of the developed FOBAMNN with multiple delays can be fairly preserved if selecting lesser control delays, and Hopf bifurcation emerges once the control delays outnumber their critical values. The derived bifurcation results are numerically testified via the bifurcation graphs. The feasibility of theoretical analysis is ultimately corroborated in the light of simulation experiments. The analytic results available in this paper are beneficial to give impetus to resolve the issues of bifurcations of high-order FONNs with multiple delays.
本文阐述了具有四种不同时滞的分数阶双向联想记忆神经网络（FOBAMNN）的分岔问题。基于确定的假设，首先将所构建的FOBAMNN转化为具有两个不同时滞的神经网络。然后，通过在转化后的模型中设定一个时滞并选择其余时滞作为分岔参数，定量计算关于不同时滞的Hopf分岔临界值。研究发现，如果选择较小的控制时滞，所构建的具有多个时滞的FOBAMNN的稳定性能够得到较好的保持，而一旦控制时滞超过其临界值，就会出现Hopf分岔。通过分岔图对所推导的分岔结果进行了数值验证。根据仿真实验最终证实了理论分析的可行性。本文所得出的分析结果有助于推动解决具有多个时滞的高阶分数阶神经网络的分岔问题。
