Changes in the criticality of Hopf bifurcations due to certain model reduction techniques in systems with multiple timescales

The Journal of Mathematical Neuroscience

Table 2 Parameter values and function definitions for the HH model, Equations (9)

$Ē_{N a} = 0.5$	$Ē_{K} = - 0.77$	$Ē_{L} = - 0.544$	$ḡ_{k} = 0.3$	$ḡ_{l} = 0.0025$
k_v = 100 mV	ε = 0.0083	τ_m = 1	τ_n = 1	τ_h = 1
$a_{n} (v) = \frac{0.01 (k_{v} v + 55)}{1 - e x p (- \frac{k_{v} v + 55}{10})}$	$a_{m} (v) = \frac{0.1 (k_{v} v + 40)}{1 - e x p (- \frac{k_{v} v + 40}{10})}$			$a_{h} (v) = 0.07 exp (\frac{- k_{v} v - 65}{20})$
$b_{n} (v) = 0.125 exp (\frac{- k_{v} v - 65}{80})$	$b_{m} (v) = 4 exp (\frac{- k_{v} v - 65}{18})$			$b_{h} (v) = \frac{1}{e x p (\frac{- k_{v} v - 35}{10}) + 1}$
$n_{\infty} (v) = \frac{a_{n} (v)}{a_{n} (v) + b_{n} (v)}$	$m_{\infty} (v) = \frac{a_{m} (v)}{a_{m} (v) + b_{m} (v)}$			$h_{\infty} (v) = \frac{a_{h} (v)}{a_{h} (v) + b_{h} (v)}$
$t_{n} (v) = \frac{1}{a_{n} (v) + b_{n} (v)}$	$t_{m} (v) = \frac{1}{a_{m} (v) + b_{m} (v)}$			$t_{h} (v) = \frac{1}{a_{h} (v) + b_{h} (v)}$