Studying the Phenomenon of Neural Bursting and Spiking in Neurons: Morris-Lecar Model

In this study, we explore the interesting phenomenon of firing spikes and complex dynamics of Morris-
Lecar model. We consider a set of parameters such that the model exhibits a wide range of
phenomenons. We investigate the influences of injected current and temperature on the spiking
dynamics of Morris-Lecar model. Moreover, we study bifurcations, and computational properties of
this neuron model. Also, we define a bound (Max and Min voltage) for membrane potential and a
certain voltage value or threshold for firing the spikes. Studying the two co-dimension bifurcations
demonstrates much more complicated behaviors for this single neuron model. We also describe the
phenomenon of neural bursting, and investigate the dynamics of Morris-Lecar model as a squarewave
burster, elliptic burster and parabolic burster. We have found new two co-dimension bifurcations
compared to two dimensional Morris-Lecar model, cusp bifurcation and zero-hopf bifurcation. We
presented the Morris-Lecar bursting model for square-wave, elliptic and parabolic burster and we
displayed the circuit model corresponding to each type of burster. Finding other types of bursting for
Morris-Lecar model can be a new research project which needs to further study about the
phenomenon of neuronal bursting.