Browsing by Author "Abobakar, Zargoun"
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Item FEEDBACK CONTROL OF SYNAPTICALLY COUPLED HODGKIN-HUXLEY NEURONS(2022-01-18) Abobakar, Zargoun; Doruk, Reşat ÖzgürThrough a gap junction (electrical synapse) a pair of identical Hodgkin-Huxley neuron models are coupled together. These neurons are excited by an external current. The system we have represented is a nonlinear electrical circuit and the gap is a synaptic conductance. The complete system is of nonlinear multi-input, multi output (MIMO) type system. By using the MATLAB based software package called MATCONT and the bifurcation theory we tracked the neuron parameters that lead to bifurcation conditions. In addition, we studied the couple of the Hodgkin-Huxley model by selected different values of the synaptic conductance. For each value of the synaptic conductance we analyzed the bifurcations for the parameters of the neurons one-by-one using MATCONT. After that, we designed a controller to stabilize oscillation in the membrane potential caused by the change the parametersof the neurons. A washout filter controller of the second order type is used. This controller provides an electrical current injection to control the unwanted behaviour of the neurons due to parametric bifurcations. Linear Quadratic Regulator (LQR) supported by projective control theory, serves as the reference method in the design of the controller. The washout filter processes the membrane potentials only and projective control generates a gain to transform the filtered output to a current injection to the slave neuron.