LQR Suppression of Hopf Bifurcation in Hodgkin- Huxley Neurons
Abed EH and Fu JH. Local feedback stabilization and bifurcation control, I. Hopf bifurcation [M]. Elsevier Science Publishers B. V. 1986.
Abed EH, Wang HO, Chen RC. Stabilization of period doubling bifurcations and implications for control of chaos [C], Decision and Control, 1994. Proceedings of the, IEEE Conference on. IEEE 1994; 4: 3287-3292.
Adrian RH and Marashall MW. Sodium currents in mammalian muscle. J Physiol 1977; 268: 223–250.
An DHU. Schizophrenia as a dynamical disease [J]. Pharmacopsychiatry 2006; 39(S 1): 36-42.
Chay TR and Cook DL. Endogenous bursting patterns in excitable cells[J]. Mathematical Biosciences 1988; 90(1): 139-153.
Chen G and Yu X. On time-delayed feedback control of chaotic systems[J]. IEEE Transactions on Circuits & Systems I Fundamental Theory & Applications 1999; 46(6): 767-772.
Dhooge A, Govaerts W, Kuznetsov YA. MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs[J]. Acm Transactions on Mathematical Software 2003; 29(2): 141-164.
Doruk RO. Control of repetitive firing in Hodgkin–Huxley nerve fibers using electric fields[J]. Chaos Solitons & Fractals 2013; 52(7): 66-72.
Doruk Ozgur. Control of Hopf Bifurcations in Hodgkin-Huxley Neurons by Automatic Temperature Manipulation [S.l.]. NeuroQuantology 2018; 16(2).
Duval A and Leoty C. Ionic currents in mammalian fast skeletal muscle. J Physiol 1978; 278: 403–423.
Fitzhugh R. Computation of Impulse Initiation and Saltatory Conduction in a Myelinated Nerve Fiber [J]. Biophysical Journal 1962; 2(1): 11-21.
Hassouneh MA, Lee HC, Abed EH. Washout filters in feedback control: benefits, limitations and extensions [C], American Control Conference, 2004. Proceedings of the. IEEE 2004; 5 :3950-3955.
Hille B. Ion channels of excitable membranes [M]. Sinauer, 2001.
Hodgkin AL and Huxley AF. Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo.J Physiol 1952;116: 449–472.
Hodgkin AL and Huxley AF. The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. J Physiol 1952; 116: 497–506.
Hodgkin AL and Huxley AF. A quantitative description of membrane and its application to conduction and excitation in nerve. J Physiol 1952; 117: 500–544.
Hodgkin AL and Huxley AF. The components of membrane conductance in the giant axon of Loligo. J Physiol 1952; 116: 473–496.
Mustafa IH, Ibrahim G, Elkamel A, Elnashaie SS, Chen P. Non-linear feedback modeling and bifurcation of the acetylcholine neurocycle and its relation to Alzheimer's and Parkinson's diseases. Chemical Engineering Science. 2009; 64(1): 69-90.
Pappone PA. Voltage-clamp experiments in normal and denervated mammalian skeletal muscle fibers. J Physiol 1980; 280: 377–410.
Thompson JMT, Stewart HB. A Tutorial Glossary of Geometrical Dynamics [J]. International Journal of Bifurcation & Chaos 1993; 3(02): 223-239.
Velazquez JL, Cortez MA, Snead III OC, Wennberg R. Dynamical regimes underlying epileptiform events: role of instabilities and bifurcations in brain activity. Physica D: Nonlinear Phenomena 2003; 186(3-4): 205-220.
Zhou S, Liao X, Wu Z, Wong KW. Hopf bifurcation in a control system for the Washout filter-based delayed neural equation. Chaos, Solitons & Fractals 2005; 23(1): 101-115.