Asymptotic behavior of Morris-Lecar system (Q933550)

The Morris-Lecar system describes the behavior of a neuron based on the flow of potassium and calcium ions. It is a system of two autonomous ordinary differential equations of the type \[ {dx\over dt}= f(x,y,\alpha),\quad {dy\over dt}= g(x,y,\alpha),\tag{\(*\)} \] where \(\alpha\) is some parameter vector. For certain parameter vector \(\alpha_0\), the authors embed \((*)\) into the family of singularly perturbed systems \[ \varepsilon{dx\over dt}= f(x,y,\alpha_0),\quad {dy\over dt}= g(x,y,\alpha) \] and claim that Tichonov's theory can be applied to explain the spiking behavior of \((*)\).