# brainpy.neurons.MorrisLecar#

class brainpy.neurons.MorrisLecar(*args, input_var=True, **kwargs)[source]#

The Morris-Lecar neuron model.

Model Descriptions

The Morris-Lecar model [4] (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 Examples

>>> import brainpy as bp
>>>
>>> group = bp.neurons.MorrisLecar(1)
>>> runner = bp.DSRunner(group, monitors=['V', 'W'], inputs=('input', 100.))
>>> runner.run(1000)
>>>
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 8)
>>> bp.visualize.line_plot(runner.mon.ts, runner.mon.W, ylabel='W')
>>> bp.visualize.line_plot(runner.mon.ts, runner.mon.V, ylabel='V', show=True)


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

__init__(*args, input_var=True, **kwargs)[source]#

Methods

 __init__(*args[, input_var]) add_aft_update(key, fun) Add the after update into this node add_bef_update(key, fun) Add the before update into this node add_inp_fun(key, fun[, label, category]) Add an input function. clear_input() Empty function of clearing inputs. cpu() Move all variable into the CPU device. cuda() Move all variables into the GPU device. dV(V, t, W, I) dW(W, t, V) get_aft_update(key) Get the after update of this node by the given key. get_batch_shape([batch_size]) get_bef_update(key) Get the before update of this node by the given key. get_delay_data(identifier, delay_pos, *indices) Get delay data according to the provided delay steps. get_delay_var(name) get_inp_fun(key) Get the input function. get_local_delay(var_name, delay_name) Get the delay at the given identifier (name). has_aft_update(key) Whether this node has the after update of the given key. has_bef_update(key) Whether this node has the before update of the given key. init_param(param[, shape, sharding]) Initialize parameters. init_variable(var_data, batch_or_mode[, ...]) Initialize variables. jit_step_run(i, *args, **kwargs) The jitted step function for running. load_state(state_dict, **kwargs) Load states from a dictionary. load_state_dict(state_dict[, warn, compatible]) Copy parameters and buffers from state_dict into this module and its descendants. nodes([method, level, include_self]) Collect all children nodes. register_delay(identifier, delay_step, ...) Register delay variable. register_implicit_nodes(*nodes[, node_cls]) register_implicit_vars(*variables[, var_cls]) register_local_delay(var_name, delay_name[, ...]) Register local relay at the given delay time. reset(*args, **kwargs) Reset function which reset the whole variables in the model (including its children models). reset_local_delays([nodes]) Reset local delay variables. reset_state([batch_size]) return_info() save_state(**kwargs) Save states as a dictionary. setattr(key, value) rtype: None state_dict(**kwargs) Returns a dictionary containing a whole state of the module. step_run(i, *args, **kwargs) The step run function. sum_current_inputs(*args[, init, label]) Summarize all current inputs by the defined input functions .current_inputs. sum_delta_inputs(*args[, init, label]) Summarize all delta inputs by the defined input functions .delta_inputs. sum_inputs(*args, **kwargs) to(device) Moves all variables into the given device. tpu() Move all variables into the TPU device. tracing_variable(name, init, shape[, ...]) Initialize the variable which can be traced during computations and transformations. train_vars([method, level, include_self]) The shortcut for retrieving all trainable variables. tree_flatten() Flattens the object as a PyTree. tree_unflatten(aux, dynamic_values) Unflatten the data to construct an object of this class. unique_name([name, type_]) Get the unique name for this object. update([x]) The function to specify the updating rule. update_local_delays([nodes]) Update local delay variables. vars([method, level, include_self, ...]) Collect all variables in this node and the children nodes.

Attributes

 after_updates before_updates cur_inputs current_inputs delta_inputs derivative implicit_nodes implicit_vars mode Mode of the model, which is useful to control the multiple behaviors of the model. name Name of the model. supported_modes Supported computing modes. varshape The shape of variables in the neuron group.