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Hopf bifurcation control of the M-L neuron model with type I
Huang, Chunli1; Sun, Wen1; Zheng, Zhigang2; Lu, Jinhu3,4; Chen, Shihua5
2017
Source PublicationNONLINEAR DYNAMICS
ISSN0924-090X
Volume87Issue:2Pages:755-766
AbstractMany neurological diseases are known to be caused by bifurcations induced by a change in the values of one or more regulating parameter of nervous systems. The bifurcation control may have potential applications in the diagnosis and therapy of these dynamical diseases. In this paper, a washout filter-aided dynamic feedback controller composed of the linear term and the nonlinear cubic term is employed to control the onset of Hopf bifurcation in the Morris-Lecar (M-L) neuron model with type I. It is shown that the linear term determines the location of the Hopf bifurcation, while the nonlinear cubic term regulates the criticality of the Hopf bifurcation, preventing it from occurring in a certain range of the externally applied current. The relationships among the externally applied current, the linear control gain and the reciprocal of the filter time constant are further systematically analyzed, which help to make the best choice from the feasible parameter space to achieve our control task. Simulation results are provided to illustrate the effectiveness of the proposed methods.
KeywordMorris-Lecar model Hopf bifurcation control Washout filter Neural diseases
DOI10.1007/s11071-016-3073-x
Language英语
Funding ProjectNational Key Research and Development Program of China[2016YFB0800401] ; National Natural Science Foundation of China[61621003] ; National Natural Science Foundation of China[61532020] ; National Natural Science Foundation of China[11472290] ; National Natural Science Foundation of China[61472027] ; National Natural Science Foundation of China[11475022] ; National Natural Science Foundation of China[11547006] ; National Natural Science Foundation of China[61503046] ; Key Program of Frontier Science of the Chinese Academy of Sciences[QYZDJ-SSW-JSC003] ; Guangxi Education Department Key Laboratory of Symbolic Computation and Engineering Data Processing[FH201502]
WOS Research AreaEngineering ; Mechanics
WOS SubjectEngineering, Mechanical ; Mechanics
WOS IDWOS:000392293200003
PublisherSPRINGER
Citation statistics
Cited Times:7[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/24515
Collection系统科学研究所
Affiliation1.Yangtze Univ, Sch Informat & Math, Jingzhou 434023, Peoples R China
2.Huaqiao Univ, Coll Informat Sci & Engn, Xiamen 361021, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
4.King Abdulaziz Univ, Fac Engn, Jeddah, Saudi Arabia
5.Wuhan Univ, Coll Math & Stat, Wuhan 430072, Peoples R China
Recommended Citation
GB/T 7714
Huang, Chunli,Sun, Wen,Zheng, Zhigang,et al. Hopf bifurcation control of the M-L neuron model with type I[J]. NONLINEAR DYNAMICS,2017,87(2):755-766.
APA Huang, Chunli,Sun, Wen,Zheng, Zhigang,Lu, Jinhu,&Chen, Shihua.(2017).Hopf bifurcation control of the M-L neuron model with type I.NONLINEAR DYNAMICS,87(2),755-766.
MLA Huang, Chunli,et al."Hopf bifurcation control of the M-L neuron model with type I".NONLINEAR DYNAMICS 87.2(2017):755-766.
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