Washout Filter Based Control of Two Hodgkin-Huxley Neurons Coupled by Electrical Synapses

Abstract

The purpose of this work is to present a bifurcation control of a coupled Hodgkin-Huxley model. The structure of the model is like a master-slave mechanism where two neurons are coupled by an electrical synaptic conductance. Fundamental aim is to stop the bursts generated due to Hopf bifurcations arisen from the injection of external current to the master (first) neuron. The bifurcations are analyzed and detected using the MATLAB based MATCONT toolbox and various Andronov-Hopf conditions are detected. The synaptic conductance appears to affect the occurrence of the Hopf conditions. Higher conductances lead to lesser number of Hopf points. The control of these bifurcations are performed by washout filter aided by linear quadratic projective control theory. 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. A detailed numerical example for one case and summary of all cases are presented. Simulations and graphical results are presented for the detailed example. Success of other cases are summarized as a table. It appears that, too small synaptic conductance values renders it difficult to attain a stable control of the bifurcations. However, one has a successful outcome for most conductance values. ©International Research Publication House.