Table 1 Details for cell dynamics
From: Interactions of multiple rhythms in a biophysical network of neurons
Variable | \(\tau _{x}\) | \(x_{\infty }\) |
|---|---|---|
(a) | ||
m (excitatory cell) | \(0.25+4.35\cdot e^{-\frac{|\mathbf{V}+10|}{10}}\) | \(( 1+e^{\frac{-\mathbf{V}-29.5}{10}} ) ^{-1}\) |
h (excitatory cell) | \(0.15+\frac{1.15}{1+e^{\frac{\mathbf{V}+33.5}{15}}}\) | \(( 1+e^{\frac{\mathbf{V}+59.4}{10.7}} ) ^{-1}\) |
m (inhibitory cell) | \(0.25+4.35\cdot e^{-\frac{|\mathbf{V}+10|}{10}}\) | \((1+e^{\frac{-\mathbf{V}-27}{11.5}} ) ^{-1}\) |
h (inhibitory cell) | \(0.225+\frac{1.125}{1+e^{\frac{\mathbf{V}+37}{15}}}\) | \((1+e^{\frac{\mathbf{V}+58.3}{6.7}} ) ^{-1}\) |
\(\mathbf{m}_{AR}\) | \((e^{-14.6-0.086\mathbf{V}}+e^{-1.87+0.07\mathbf{V}} )^{-1}\) | \(( 1+e^{\frac{\mathbf{V}-V_{0}}{5.5}} )^{-1}\) |
Variable | \(\alpha _{x}\) | \(\beta _{x}\) |
|---|---|---|
(b) | ||
\(\mathbf{m}_{KM}\) | \(\frac{0.02}{1+e^{\frac{-\mathbf{V}-20}{5}}}\) | \(0.01e^{\frac{-\mathbf{V}-43}{18}}\) |
\(\mathbf{m}_{CaH}\) | \(\frac{4.8}{1+e^{-0.072(\mathbf{V}-5)}}\) | \(\frac{0.06(\mathbf{V}+8.9)}{e^{\frac{\mathbf{V}+8.9}{5}}-1}\) |
Function | Expression |
|---|---|
(c) | |
\(m_{0}(\mathbf{V})\) (exc. cell) | \((1+e^{\frac{-\mathbf{V}-34.5}{10}} ) ^{-1}\) |
\(m_{0}(\mathbf{V})\) (inh. cell) | \((1+e^{\frac{-\mathbf{V}-38}{10}} )^{-1}\) |