Abstract
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 square-wave burster, elliptic burster and parabolic burster.
Highlights
During recent decades, understanding the brain function and exploring its molecular and cellular mechanisms were one of the greatest challenges in different fields of science
In this paper we studied spiking dynamics of a single neuron model which is a reduction of well-known Hodgkin-Huxley model and consists of a system of ordinary differential equations
We numerically discovered the hopf bifurcation, SNLC bifurcation and homocinic bifurcation and we presented their normal form for each case separately
Summary
During recent decades, understanding the brain function and exploring its molecular and cellular mechanisms were one of the greatest challenges in different fields of science. In 1948 Hodgkin injected a dc-current of varying amplitude, and discovered that some preparations could show repetitive spiking activities with arbitrarily low frequencies, while the others discharged in a narrow frequency band [1] [5] [6] [7]. This finding was widely ignored by the scientists until 1989 when Rinzel and Ermentrout published a seminal paper and showed that the difference in behavior is because of different bifurcation mechanisms of excitability [1] [8] [9]. We look at the complicated dynamics of Morris-Lecar model as a burster
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