Stability and bifurcation control of a neuron system under a novel fractional-order PD controller  

作　　者：SHI Shuo XIAO Min RONG LiNa ZHENG WeiXing TAO BinBin CHENG ZunShui XU FengYu 

机构地区：[1]School of Automation,Nanjing University of Posts and Telecommunications,Nanjing 210003,China [2]School of Mathematics and Physics,Qingdao University of Science and Technology,Qingdao 266061,China [3]School of Computing,Engineering and Mathematics,Western Sydney Universit,Penrith NSW 2751,Australia

出　　处：《Science China(Technological Sciences)》2019年第12期2120-2129,共10页中国科学（技术科学英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos. 61573194, 51775284);the Natural Science Foundation of Jiangsu Province of China(Grant Nos. BK20181389, BK20171441);the Key Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province(Grant No. 2018SJZDI142);the Australian Research Council(Grant No. DP120104986)

摘　　要：In this paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative(PD) feedback controller, this paper aims to control the stability and Hopf bifurcation through adjusting the control gain parameters. The order chosen in PD controller is different with that of the integer-order neuron system. Sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed for the controlled neuron system. Finally,numerical simulation results are illustrated to verify our theoretical derivations and the relationships between the onset of the Hopf bifurcation and the gain parameters are obtained.In this paper, we address the problem of bifurcation control for a delayed neuron system. By introducing a new fractional-order Proportional-Derivative(PD) feedback controller, this paper aims to control the stability and Hopf bifurcation through adjusting the control gain parameters. The order chosen in PD controller is different with that of the integer-order neuron system. Sufficient conditions for guaranteeing the stability and generating Hopf bifurcation are constructed for the controlled neuron system. Finally,numerical simulation results are illustrated to verify our theoretical derivations and the relationships between the onset of the Hopf bifurcation and the gain parameters are obtained.

关 键 词：Hopf bifurcation fractional-order PD controller neuron system time delay 

分 类 号：O17[理学—数学]