Neuronal Spiking Patterns of Fractional-order Morris-Lecar Model
Fractional calculus is a novel method for studying biological and physical processes that include memory effects. Fractional calculus examines the nonlinear behaviour of physical and biological systems with varying degrees of fractionality or fractality using differential and integral operators, including non-integer orders. Because the fractional derivative can better describe the long memory features of neural responses, we expand the integer-order Morris-Lecar model in the fractional-order domain to better characterise neuron dynamics in this work. The fractional calculus was used to create this novel mathematical model to examine the complicated spiking patterns of fractional-order Morris-Lecar neural systems. We compare the findings to the Morris-Lecar model with integer order. These equations do not have analytical solutions that may be found explicitly. As a result, in order to discover the dynamical characteristics of solutions. We employed numerical and approximation approaches. Morris-Lecar reproduces quiescent, spiking, and bursting activities in the same way as its original model, but with a greater input current, depending on the different parameter values for the fractional-order Morris-Lecar. For varied input current and derivative orders, we numerically uncover the hopf bifurcation, saddle node bifurcation of limit cycle, and homocinic bifurcation for this model. Using the benefits of the fractional order derivative, we establish distinct classes of this model for a range of orders, allowing us to better extract all of the intricate dynamics of this single neuron model.
Department of Mechanical Engineering, Florida State University, Florida, USA.
College of Veterinary Medicine, Iowa State University, Iowa, USA.
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