Bifurcation control of fractional neural networks with hybrid time delay based on fractional PD control
LUAN Yi-feng
XIAO Min
ZHAO Jing
WANG Zhen
Abstract：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.
Keywords：Hopf bifurcationdistributed time delayfractional orderfractional order PD controlneural network
Publication Date：2024-10-28
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：10( 1791-1800 )