时滞Hopfield神经网络的分岔控制

 研究了一类带3个时滞的Hopfield神经网络的分岔控制问题。考虑系数扰动影响，通过对比一般的时滞状态反馈控制，根据Hopf分岔定理，选取时滞为分岔参数，提出了一类新的混合控制策略——带参数扰动和时滞状态反馈的控制方法，得到了一些新的分岔控制结果。进而通过已有结果检验分岔控制的效果，得到新的分岔控制对于改变分岔发生的位置有较好的调节和延迟的作用。这一结果对控制周期分岔和混沌行为具有重要的指导意义。最后，结合示例和数值模拟进一步验证了此混合控制策略的有效性。

Bifurcation Control for Delayed Hopfield Neural Networks

In recent years, bifurcation control has attracted many researchers from various disciplines. The aim of bifurcation control is to design a controller to modify the bifurcation properties of a given nonlinear system, and achieve desirable dynamical behaviors. The bifurcation control of a class of Hopfield neural network with three delays is investigated. In contrast to the general time-delayed state feedback control, based on the Hopf bifurcation theory and the choice of time delay as the bifurcation parameter, a new hybrid control strategy is proposed, in which the time-delayed state feedback and parameter perturbation are used to control the Hopf bifurcation of the model, and some new conclusions are obtained. In addition, we examine the effects of coefficient perturbation. Furthermore, known results are used to check the conclusions, and the new conclusions are shown to be helpful in changing and delaying the evolution of bifurcation, which has applications in a variety of areas such as controlling period bifurcation and chaos. Finally, we use examples and numerical-simulation results to confirm that the hybrid controller using time delay is an efficient means to control Hopf bifurcation.