# MorrisLecarLTC#

class brainpy.dyn.MorrisLecarLTC(size, sharding=None, keep_size=False, mode=None, name=None, method='exp_auto', init_var=True, V_Ca=130.0, g_Ca=4.4, V_K=-84.0, g_K=8.0, V_leak=-60.0, g_leak=2.0, C=20.0, V1=-1.2, V2=18.0, V3=2.0, V4=30.0, phi=0.04, V_th=10.0, W_initializer=OneInit(value=0.02), V_initializer=Uniform(min_val=-70.0, max_val=-60.0, rng=[ 479025946 4206239744]))[source]#

The Morris-Lecar neuron model with liquid time constant.

Model Descriptions

The Morris-Lecar model  (Also known as $$I_{Ca}+I_K$$-model) is a two-dimensional “reduced” excitation model applicable to systems having two non-inactivating voltage-sensitive conductances. This model was named after Cathy Morris and Harold Lecar, who derived it in 1981. Because it is two-dimensional, the Morris-Lecar model is one of the favorite conductance-based models in computational neuroscience.

The original form of the model employed an instantaneously responding voltage-sensitive Ca2+ conductance for excitation and a delayed voltage-dependent K+ conductance for recovery. The equations of the model are:

\begin{split}\begin{aligned} C\frac{dV}{dt} =& - g_{Ca} M_{\infty} (V - V_{Ca})- g_{K} W(V - V_{K}) - g_{Leak} (V - V_{Leak}) + I_{ext} \\ \frac{dW}{dt} =& \frac{W_{\infty}(V) - W}{ \tau_W(V)} \end{aligned}\end{split}

Here, $$V$$ is the membrane potential, $$W$$ is the “recovery variable”, which is almost invariably the normalized $$K^+$$-ion conductance, and $$I_{ext}$$ is the applied current stimulus.

Model Parameters

 Parameter Init Value Unit Explanation V_Ca 130 mV Equilibrium potentials of Ca+.(mV) g_Ca 4.4 Maximum conductance of corresponding Ca+.(mS/cm2) V_K -84 mV Equilibrium potentials of K+.(mV) g_K 8 Maximum conductance of corresponding K+.(mS/cm2) V_Leak -60 mV Equilibrium potentials of leak current.(mV) g_Leak 2 Maximum conductance of leak current.(mS/cm2) C 20 Membrane capacitance.(uF/cm2) V1 -1.2 Potential at which M_inf = 0.5.(mV) V2 18 Reciprocal of slope of voltage dependence of M_inf.(mV) V3 2 Potential at which W_inf = 0.5.(mV) V4 30 Reciprocal of slope of voltage dependence of W_inf.(mV) phi 0.04 A temperature factor. (1/s) V_th 10 mV The spike threshold.

References

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

Reset function which resets local states in this model.

Simply speaking, this function should implement the logic of resetting of local variables in this node.

supported_modes: Optional[Sequence[bm.Mode]] = (<class 'brainpy._src.math.modes.NonBatchingMode'>, <class 'brainpy._src.math.modes.BatchingMode'>)#

Supported computing modes.

update(x=None)[source]#

The function to specify the updating rule.