Analysis and control of the bifurcation of Hodgkin–Huxley model |
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Institution: | 1. Department of Computer Engineering, Bartın University, 74600 Bartın, Turkey;2. Department of Biomedical Engineering, Zonguldak Bulent Ecevit University,67100 Zonguldak, Turkey;1. School of Computing, Electronic and Mathematics, Plymouth University, Plymouth, UK;2. Departament de Matemàtica, Universitat de Lleida, Av. Jaume II, 69, Lleida, Catalonia 25001, Spain |
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Abstract: | The Hodgkin–Huxley (HH) equations are parameterized by a number of parameters and show a variety of qualitatively different behaviors depending on the various parameters. This paper finds the bifurcation would occur when the leakage conductance gl is lower than a special value. The Hopf bifurcation of HH model is controlled by applying a simple and unified state-feedback method and the bifurcation point is moved to an unreachable physiological point at the same time, so in this way an absolute bifurcation control is achieved. The simulation results demonstrate the validity of such theoretic analysis and control method. This new method could be a great help to the design of new closed-loop electrical stimulation systems for patients suffering from different nerve system dysfunctions. |
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