HH

HH#

class brainpy.state.HH(in_size, ENa=Quantity(50., "mV"), gNa=Quantity(120., "mS"), EK=Quantity(-77., "mV"), gK=Quantity(36., "mS"), EL=Quantity(-54.387, "mV"), gL=Quantity(0.03, "mS"), V_th=Quantity(20., "mV"), C=Quantity(1., "uF"), V_initializer=Uniform(low=-70. mV, high=-60. mV), m_initializer=None, h_initializer=None, n_initializer=None, spk_fun=ReluGrad(alpha=0.3, width=1.0), spk_reset='soft', name=None)#

Hodgkin–Huxley neuron model.

Model Descriptions

The Hodgkin-Huxley (HH; Hodgkin & Huxley, 1952) model for the generation of the nerve action potential is one of the most successful mathematical models of a complex biological process that has ever been formulated. The basic concepts expressed in the model have proved a valid approach to the study of bio-electrical activity from the most primitive single-celled organisms such as Paramecium, right through to the neurons within our own brains.

Mathematically, the model is given by,

\[C \frac{dV}{dt} = -(\bar{g}_{Na} m^3 h (V-E_{Na}) + \bar{g}_K n^4 (V-E_K) + g_{leak} (V - E_{leak})) + I(t)\]
\[\frac{dx}{dt} = \alpha_x (1-x) - \beta_x, \quad x\in \{m, h, n\}\]

where

\[\alpha_m(V) = \frac{0.1(V+40)}{1-\exp\!\left(\frac{-(V + 40)}{10}\right)}\]
\[\beta_m(V) = 4.0 \exp\!\left(\frac{-(V + 65)}{18}\right)\]
\[\alpha_h(V) = 0.07 \exp\!\left(\frac{-(V+65)}{20}\right)\]
\[\beta_h(V) = \frac{1}{1 + \exp\!\left(\frac{-(V + 35)}{10}\right)}\]
\[\alpha_n(V) = \frac{0.01(V+55)}{1-\exp(-(V+55)/10)}\]
\[\beta_n(V) = 0.125 \exp\!\left(\frac{-(V + 65)}{80}\right)\]
Parameters:

  • in_size (Size) – Size of the input to the neuron.

  • ENa (ArrayLike, default 50. * u.mV) – Reversal potential of sodium.

  • gNa (ArrayLike, default 120. * u.msiemens) – Maximum conductance of sodium channel.

  • EK (ArrayLike, default -77. * u.mV) – Reversal potential of potassium.

  • gK (ArrayLike, default 36. * u.msiemens) – Maximum conductance of potassium channel.

  • EL (ArrayLike, default -54.387 * u.mV) – Reversal potential of leak channel.

  • gL (ArrayLike, default 0.03 * u.msiemens) – Conductance of leak channel.

  • V_th (ArrayLike, default 20. * u.mV) – Threshold of the membrane spike.

  • C (ArrayLike, default 1.0 * u.ufarad) – Membrane capacitance.

  • V_initializer (Callable) – Initializer for membrane potential.

  • m_initializer (Callable, optional) – Initializer for m channel. If None, uses steady state.

  • h_initializer (Callable, optional) – Initializer for h channel. If None, uses steady state.

  • n_initializer (Callable, optional) – Initializer for n channel. If None, uses steady state.

  • spk_fun (Callable, default surrogate.ReluGrad()) – Surrogate gradient function.

  • spk_reset (str, default 'soft') – Reset mechanism after spike generation.

  • name (str, optional) – Name of the neuron layer.

V#

Membrane potential.

Type:

HiddenState

m#

Sodium activation variable.

Type:

HiddenState

h#

Sodium inactivation variable.

Type:

HiddenState

n#

Potassium activation variable.

Type:

HiddenState

See also

MorrisLecar

Two-dimensional reduced excitation model.

WangBuzsakiHH

Modified HH model for hippocampal interneurons.

Notes

  • The Hodgkin-Huxley model is the foundation of biophysical neuron modeling [1].

  • This implementation uses exponential Euler integration for numerical stability.

  • For more information about the model, see [2].

References

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create an HH neuron layer with 10 neurons
>>> hh = brainpy.state.HH(10)
>>> # Initialize the state
>>> hh.init_state(batch_size=1)
>>> # Apply an input current and update the neuron state
>>> spikes = hh.update(x=10.*u.uA)
get_spike(V=None)[source]#

Generate spikes based on neuron state variables.

This abstract method must be implemented by subclasses to define the spike generation mechanism. The method should use the surrogate gradient function self.spk_fun to enable gradient-based learning.

Parameters:

  • *args – Positional arguments (typically state variables like membrane potential)

  • **kwargs – Keyword arguments

Returns:

Binary spike tensor where 1 indicates a spike and 0 indicates no spike.

Return type:

ArrayLike

Raises:

NotImplementedError – If the subclass does not implement this method.

init_state(batch_size=None, **kwargs)[source]#

State initialization function.

reset_state(batch_size=None, **kwargs)[source]#

State resetting function.