Impact of Chloride Channel on Firing Patterns of the Fractional-order Morris-Lecar Model

Abstract

Fractional calculus as a new approach for modeling has been used widely to study the non-linear behavior of physical and biological systems with some degrees of fractionality or fractality using differential and integral operators with non integerorders. In this paper, to explore different dynamical classes of the Morris-Lecar neuronal model with chloride channel, we extend its integer-order domain into a new fractional-order space using fractional calculus. The nonstandard finite difference (NSFD) method following the Grnwald Letnikov discretization may be applied to discretize the model and obtain the fractional-order form. Fractional derivative order has been used as a new control parameter to extract variety of neuronal firing patterns that happen in real world application but the integer-order operator may not be able to reveal them. To find the impact of chloride channel on dynamical behaviors of this neuronal model, the phase portrait and time series analysis have been performed for different fractional-orders and input currents. Depending on different values for , the fractional-order Morris-Lecar model with a chloride channel reproduces quiescent, spiking and bursting activities the same as the fractionalorder Morris-Lecar model without a chloride channel. We numerically discover the occurrence of hopf bifurcation, and homoclinic bifurcation for these two models. These results show that adding a chloride channel to this neuron does not affect the overall spiking patterns of the model, however, when we add this new ionic channel, the neuron needs higher input current as stimulus to fire action potential and spike.