Evaluating the Impact of Chloride Channel on Spiking Patterns of Morris-Lecar Model

In this paper, we study the complicated dynamics of general Morris-Lecar model with the impact of
fluctuations on firing patterns of this neuron model. After adding channel to the original
Morris-Lecar model, we see that the dynamics of the original model such as its bifurcations of
equilibrium points would be changed and they would occur at different values compare to the primary
model. We discover these qualitative changes in the point of dynamical systems and Neuroscience.
We will conduct the two co-dimension bifurcations analysis with respect to different control
parameters to explore the complicated behaviors for this new neuron model. Period doubling
bifurcation is a bifurcation for which a new limit cycle creates from the limit cycle that exists and the
period of the new limit cycle is twice of the first limit cycle. Moreover, we have shown changing the
type of Hopf bifurcation from supercritical to subcritical which means that the type of stability changes
from monostability in supercritical to bistability in subcritical Hopf bifurcation.