brainpy.neurons.HindmarshRose

brainpy.neurons.HindmarshRose#

class brainpy.neurons.HindmarshRose(size, a=1.0, b=3.0, c=1.0, d=5.0, r=0.01, s=4.0, V_rest=-1.6, V_th=1.0, V_initializer=ZeroInit, y_initializer=OneInit(value=-10.0), z_initializer=ZeroInit, noise=None, method='exp_auto', keep_size=False, input_var=True, name=None, mode=None, spike_fun=<brainpy._src.math.surrogate._utils.VJPCustom object>)[source]#

Hindmarsh-Rose neuron model.

Model Descriptions

The Hindmarsh–Rose model [1] [2] of neuronal activity is aimed to study the spiking-bursting behavior of the membrane potential observed in experiments made with a single neuron.

The model has the mathematical form of a system of three nonlinear ordinary differential equations on the dimensionless dynamical variables \(x(t)\), \(y(t)\), and \(z(t)\). They read:

\[\begin{split}\begin{aligned} \frac{d V}{d t} &= y - a V^3 + b V^2 - z + I \\ \frac{d y}{d t} &= c - d V^2 - y \\ \frac{d z}{d t} &= r (s (V - V_{rest}) - z) \end{aligned}\end{split}\]

where \(a, b, c, d\) model the working of the fast ion channels, \(I\) models the slow ion channels.

Model Examples

>>> import brainpy.math as bm
>>> import brainpy as bp
>>> import matplotlib.pyplot as plt
>>>
>>> bp.math.set_dt(dt=0.01)
>>> bp.ode.set_default_odeint('rk4')
>>>
>>> types = ['quiescence', 'spiking', 'bursting', 'irregular_spiking', 'irregular_bursting']
>>> bs = bm.array([1.0, 3.5, 2.5, 2.95, 2.8])
>>> Is = bm.array([2.0, 5.0, 3.0, 3.3, 3.7])
>>>
>>> # define neuron type
>>> group = bp.neurons.HindmarshRose(len(types), b=bs)
>>> runner = bp.DSRunner(group, monitors=['V'], inputs=['input', Is],)
>>> runner.run(1e3)
>>>
>>> fig, gs = bp.visualize.get_figure(row_num=3, col_num=2, row_len=3, col_len=5)
>>> for i, mode in enumerate(types):
>>>     fig.add_subplot(gs[i // 2, i % 2])
>>>     plt.plot(runner.mon.ts, runner.mon.V[:, i])
>>>     plt.title(mode)
>>>     plt.xlabel('Time [ms]')
>>> plt.show()

Model Parameters

Parameter

Init Value

Unit

Explanation

a

1

Model parameter. Fixed to a value best fit neuron activity.

b

3

Model parameter. Allows the model to switch between bursting and spiking, controls the spiking frequency.

c

1

Model parameter. Fixed to a value best fit neuron activity.

d

5

Model parameter. Fixed to a value best fit neuron activity.

r

0.01

Model parameter. Controls slow variable z’s variation speed. Governs spiking frequency when spiking, and affects the number of spikes per burst when bursting.

s

4

Model parameter. Governs adaption.

Model Variables

Member name

Initial Value

Explanation

V

-1.6

Membrane potential.

y

-10

Gating variable.

z

0

Gating variable.

spike

False

Whether generate the spikes.

input

0

External and synaptic input current.

t_last_spike

-1e7

Last spike time stamp.

References

__init__(size, a=1.0, b=3.0, c=1.0, d=5.0, r=0.01, s=4.0, V_rest=-1.6, V_th=1.0, V_initializer=ZeroInit, y_initializer=OneInit(value=-10.0), z_initializer=ZeroInit, noise=None, method='exp_auto', keep_size=False, input_var=True, name=None, mode=None, spike_fun=<brainpy._src.math.surrogate._utils.VJPCustom object>)[source]#

Methods

__init__(size[, a, b, c, d, r, s, V_rest, ...])

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, y, z, I_ext)

dy(y, t, V)

dz(z, 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()

rtype:

Union[Variable, ReturnInfo]

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.