The classical biophysical Morris-Lecar model of neuronal excitability predicts that upon stimulation of the neuron with a sufficiently large constant depolarizing current there exists a finite interval of the current values where periodic spike generation occurs. Above the upper boundary of this interval there is a four-stage damping of the spike amplitude: 1) minor primary damping, which reflects a typical transient to stationary  state, 2) plateau of nearly undamped periodic oscillations, 3) strong damping, and 4) reaching a constant stationary asymptotic value V_{st of the neuron potential. We have linearized the Morris-Lecar model equations at the vicinity of V_{st equations can be reduced to a standard equation for exponentially damped harmonic oscillations. Importantly, all coefficients of this equation can be explicitly expressed through parameters of the original Morris-Lecar model, enabling direct comparison (i.e. without any fitting) of the numerical and analytical solutions for the neuron potential dynamics at later stages of the spike amplitude damping. This allows to explore quantitatively the applicability boundary of linear stability analysis that implies exponential damping.
The classical biophysical Morris-Lecar model of neuronal excitability predicts that upon stimulation of the neuron with a sufficiently large constant depolarizing current there exists a finite interval of the current values where periodic spike generation occurs. Above the upper boundary of this interval , there is four-stage damping of the spike amplitude: 1) minor primary damping, which reflects a typical transient to stationary dynamic state, 2) plateau of nearly undamped periodic oscillations, 3) strong damping, and 4) reaching a constant asymptotic value of the neuron potential. We have shown that in the vicinity of the asymptote the Morris-Lecar equations can be reduced to the standard equation for exponentially damped harmonic oscillations. Importantly, all coefficients of this equation can be explicitly expressed through parameters of the original Morris-Lecar model, enabling direct comparison of the numerical and analytical solutions for the neuron potential dynamics at later stages of the spike amplitude damping.
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stationary asymptotic value V_{st
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linearized the
shown that in the vicinity of the asymptote the
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model equations at the vicinity of V_{st
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the
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(i.e. without any fitting)
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damping. This allows to explore quantitatively the applicability boundary of linear stability analysis that implies exponential