AM  Vol.11 No.7 , July 2020
Impact of Chloride Channel on Spiking Patterns of Morris-Lecar Model
Abstract: In this paper,we study the complicated dynamics of general Morris-Lecar model with the impact of Cl- fluctuations on firing patterns of this neuron model. After adding Cl- channel in the original Morris-Lecar model, the dynamics of the original model such as its bifurcations of equilibrium points would be changed and they occurred at different values compared to the primary model. We discover these qualitative changes in the point of dynamical systems and neuroscience. We will conduct the co-dimension two bifurcations analysis with respect to different control parameters to explore the complicated behaviors for this new neuron model.
Cite this paper: Azizi, T. and Alali, B. (2020) Impact of Chloride Channel on Spiking Patterns of Morris-Lecar Model. Applied Mathematics, 11, 650-669. doi: 10.4236/am.2020.117044.

[1]   Izhikevich, E.M. (2007) Dynamical Systems in Neuroscience. MIT Press, Cambridge.

[2]   Izhikevich, E.M. (2003) Simple Model of Spiking Neurons. IEEE Transactions on Neural Networks, 14, 11569-1572.

[3]   Izhikevich, E.M. (2004) Which Model to Use for Cortical Spiking Neurons? IEEE Transactions on Neural Networks, 15, 1063-1070.

[4]   Izhikevich, E.M. (2000) Neural Excitability, Spiking and Bursting. International Journal of Bifurcation and Chaos, 10, 1171-1266.

[5]   Cai, R., Liu, Y.C., Duan, J.Q. and Abebe, A.T. (2020) State Transitions in the Morris-Lecar Model under Stable Lévy Noise. The European Physical Journal B, 93, 1-9.

[6]   Rinzel, J. and Ermentrout, G.B. (1989) Analysis of Neural Excitability and Oscillations. MIT Press, Cambridge.

[7]   Ermentrout, G.B. and Terman, D.H. (2010) Mathematical Foundations of Neuroscience. Springer Science & Business Media, Berlin, 35.

[8]   Ermentrout, B. (1996) Type I Membranes, Phase Resetting Curves, and Synchrony. Neural Computation, 8, 979-1001.

[9]   Hodgkin, A.L. and Huxley, A.F. (1952) A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve. The Journal of Physiology, 117, 500-544.

[10]   Hodgkin, A.L. (1948) The Local Electric Changes Associated with Repetitive Action in a Non-Medullated Axon. The Journal of Physiology, 107, 165-181.

[11]   Morris, C. and Lecar, H. (1981) Voltage Oscillations in the Barnacle Giant Muscle Fiber. Biophysical Journal, 35, 193-213.

[12]   Azizi, T. and Mugabi, R. (2020) The Phenomenon of Neural Bursting and Spiking in Neurons: Morris-Lecar Model. Applied Mathematics, 11, 203-226.

[13]   FitzHugh, R. (1961) Impulses and Physiological States in Theoretical Models of Nerve Membrane. Biophysical Journal, 1, 445-466.

[14]   Kuznetsov, Y.A. (2013) Elements of Applied Bifurcation Theory. Springer Science & Business Media, Berlin, 112.

[15]   Wiggins, S. (2003) Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer Science & Business Media, Berlin, 2.