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
()save_state
(**kwargs)Save states as a dictionary.
setattr
(key, value)- rtype:
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.