DOI: 10.14704/nq.2019.17.2.1961

LQR Suppression of Hopf Bifurcation in Hodgkin- Huxley Neurons

Yexin lin, Haiyuan Liu, Li Hu


The work of Hodgkin and Huxley on nerve conduction has long been recognized as an outstanding scientific achievement. The Hodgkin-Huxley equations are modeled by a number of parameters and perform diverse behaviors depending on the various parameters. The purpose of this research is to solve the bifurcation control problem in the Hodgkin-Huxley nerve fibers. In this study, we focus on the Hopf bifurcation in the HH model, which arises by the external current injection. We present a feedback controlled approach to control the bifurcation phenomenon in the Hodgkin-Huxley nerve fibers via washout filter which can stop the repetitive firing in a particular region of the nervous system validly. A washout filter is augmented to the HH dynamics and the output of the filter is fed to an external controller generator through a linear gain. The linear projective control theory is applied to compute the control gain. The stable controller is performed by two similar control rules that are designed by the integration of the washout filters and static projective control theory. The first case of the control rule filters all the dynamic variables including the membrane potential and the channel activation, while the second case of the control rule filters merely the membrane potential. The MATCONT software package is used for analysis of the bifurcation points in conjunction with MATLAB.


Hodgkin-Huxley model, Hopf bifurcation, Washout filter, Bifurcation control

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