基于分数阶PD控制的分数阶混杂时滞神经网络分岔控制

Bifurcation control of fractional neural networks with hybrid time delay based on fractional PD control

本文提出了一个具有离散和分布时滞的分数阶神经网络系统,并运用分数阶PD控制器对其进行分岔控制.本文创新之处在于将分数阶引入了一个含离散与分布时滞的双神经元网络系统,并通过在原网络中引入一个虚拟神经元,形成了一个仅涉及离散时滞的新三神经元网络.引入了分数阶PD控制器得到受控系统,采用离散时滞之和作为分岔参数,证明了Hopf分岔的存在性,并通过分数阶PD控制策略实现了对分岔阈值点的控制.研究发现,通过选取合适的控制参数,分数阶PD控制器可以有效地控制系统分岔临界值.此外,各个控制器参数对于系统分岔阈值点的影响效果也被给出.

A fractional order neural network system with discrete and distributed time delays is proposed,and its bifurcation control is carried out by using the fractional-order PD controller.The innovation is that the fractional order is introduced into a two-neuron network system with discrete and distributed delays,and by introducing a virtual neuron into the original network,a new three-neuron network only involving the discrete delay is formed.The controlled system is obtained by adopting the fractional order PD controller.The existence of Hopf bifurcation is proved by using the sum of discrete time delays as bifurcation parameters,and the control of the bifurcation threshold point is achieved by the fractional order PD control strategy.It is found that the fractional order PD controller can effectively control the bifurcation critical value of system by selecting appropriate control parameters.In addition,the influence of each controller parameter on the bifurcation threshold point is also given.