Neuron models and groups¶
The Equations
object¶

class
brian.
Equations
(expr='', level=0, **kwds)¶ Container that stores equations from which models can be created
Initialised as:
Equations(expr[,level=0[,keywords...]])
with arguments:
expr
 An expression, which can each be a string representing equations,
an
Equations
objects, or a list of strings andEquations
objects. See below for details of the string format. level
 Indicates how many levels back in the stack the namespace for string
equations is found, so that e.g.
level=0
looks in the namespace of the function where theEquations
object was created,level=1
would look in the namespace of the function that called the function where theEquations
object was created, etc. Normally you can just leave this out. keywords
 Any sequence of keyword pairs
key=value
where the stringkey
in the string equations will be replaced withvalue
which can be either a string, value orNone
, in the latter case a unique name will be generated automatically (but it won’t be pretty).
Systems of equations can be defined by passing lists of
Equations
to a newEquations
object, or by addingEquations
objects together (the usage is similar to that of a Pythonlist
).String equations
String equations can be of any of the following forms:
dx/dt = f : unit
(differential equation)x = f : unit
(equation)x = y
(alias)x : unit
(parameter)
Here each of
x
andy
can be any valid Python variable name,f
can be any valid Python expression, andunit
should be the unit of the correspondingx
. You can also include multiline expressions by appending a\
character at the end of each line which is continued on the next line (following the Python standard), or comments by including a#
symbol.These forms mean:
 Differential equation
 A differential equation with variable
x
which has physical unitsunit
. The variablex
will become one of the state variables of the model.  Equation
 An equation defining the meaning of
x
can be used for building systems of complicated differential equations.  Alias
 The variable
x
becomes equivalent to the variabley
, useful for connecting two separate systems of equations together.  Parameter
 The variable
x
will have physical unitsunit
and will be one of the state variables of the model (but will not evolve dynamically, instead it should be set by the user).
Noise
String equations can also use the reserved term
xi
for a Gaussian white noise with mean 0 and variance 1.Example usage
eqs=Equations(''' dv/dt=(uv)/tau : volt u=3*v : volt w=v ''')
Details
For more details, see More on equations in the user manual.
For information on integration methods, and the StateUpdater
class, see Integration.
The NeuronGroup
object¶

class
brian.
NeuronGroup
(N, model=None, threshold=None, reset=NoReset(), init=None, refractory=0.0 * second, level=0, clock=None, order=1, implicit=False, unit_checking=True, max_delay=0.0 * second, compile=False, freeze=False, method=None, max_refractory=None)¶ Group of neurons
Initialised with arguments:
N
 The number of neurons in the group.
model
 An object defining the neuron model. It can be
an
Equations
object, a string defining anEquations
object, aStateUpdater
object, or a list or tuple ofEquations
and strings. threshold=None
 A
Threshold
object, a function, a scalar quantity or a string. Ifthreshold
is a function with one argument, it will be converted to aSimpleFunThreshold
, otherwise it will be aFunThreshold
. Ifthreshold
is a scalar, then a constant single valued threshold with that value will be used. In this case, the variable to apply the threshold to will be guessed. If there is only one variable, or if you have a variable named one ofV
,Vm
,v
orvm
it will be used. Ifthreshold
is a string then the appropriate threshold type will be chosen, for example you could dothreshold='V>10*mV'
. The string must be a one line string. reset=None
 A
Reset
object, a function, a scalar quantity or a string. If it’s a function, it will be converted to aFunReset
object. If it’s a scalar, then a constant single valued reset with that value will be used. In this case, the variable to apply the reset to will be guessed. If there is only one variable, or if you have a variable named one ofV
,Vm
,v
orvm
it will be used. Ifreset
is a string it should be a series of expressions which are evaluated for each neuron that is resetting. The series of expressions can be multiline or separated by a semicolon. For example,reset=`Vt+=5*mV; V=Vt'
. Statements involvingif
constructions will often not work because the code is automatically vectorised. For such constructions, use a function instead of a string. refractory=0*ms
,min_refractory
,max_refractory
 A refractory period, used in combination with the
reset
value if it is a scalar. For constant resets only, you can specify refractory as an array of length the number of elements in the group, or as a string, giving the name of a state variable in the group. In the case of these variable refractory periods, you should specifymin_refractory
(optional) andmax_refractory
(required). level=0
 See
Equations
for details. clock
 A clock to use for scheduling this
NeuronGroup
, if omitted the default clock will be used. order=1
 The order to use for nonlinear differential equation solvers. TODO: more details.
implicit=False
 Whether to use an implicit method for solving the differential equations. TODO: more details.
max_delay=0*ms
 The maximum allowable delay (larger values use more memory). This doesn’t usually need to be specified because Connections will update it.
compile=False
 Whether or not to attempt to compile the differential equation
solvers (into Python code). Typically, for best performance, both
compile
andfreeze
should be set toTrue
for nonlinear differential equations. freeze=False
 If True, parameters are replaced by their values at the time of initialization.
method=None
 If not None, the integration method is forced. Possible values are linear, nonlinear, Euler, exponential_Euler (overrides implicit and order keywords).
unit_checking=True
 Set to
False
to bypass unitchecking.
Methods

subgroup
(N)¶ Returns the next sequential subgroup of
N
neurons. See the section on subgroups below.

state
(var)¶ Returns the array of values for state variable
var
, with length the number of neurons in the group.

rest
()¶ Sets the neuron state values at rest for their differential equations.
The following usages are also possible for a group
G
:G[i:j]
 Returns the subgroup of neurons from
i
toj
. len(G)
 Returns the number of neurons in
G
. G.x
 For any valid Python variable name
x
corresponding to a state variable of the theNeuronGroup
, this returns the array of values for the state variablex
, as for thestate()
method above. WritingG.x = arr
forarr
aTimedArray
will set the values of variable x to bearr(t)
at time t. SeeTimedArraySetter
for details.
Subgroups
A subgroup is a view on a group. It isn’t a new group, it’s just a convenient way of referring to a subset of the neurons in an already defined group. The subset has to be a continguous set of neurons. They can be overlapping if defined with the slice notation, or consecutive if defined with the
subgroup()
method. Subgroups can themselves be subgrouped. Subgroups can be used in almost all situations exactly as if they were groups, except that they cannot be passed to theNetwork
object.Details
TODO: details of other methods and properties for people wanting to write extensions?
Resets¶
Reset objects are called each network update step to reset specified state variables of neurons that have fired.

class
brian.
Reset
(resetvalue=0.0 * volt, state=0)¶ Resets specified state variable to a fixed value
Initialise as:
R = Reset([resetvalue=0*mvolt[, state=0]])
with arguments:
resetvalue
 The value to reset to.
state
 The name or number of the state variable to reset.
This will reset all of the neurons that have just spiked. The given state variable of the neuron group will be set to value
resetvalue
.

class
brian.
StringReset
(expr, level=0)¶ Reset defined by a string
Initialised with arguments:
expr
 The string expression used to reset. This can include
multiple lines or statements separated by a semicolon.
For example,
'V=70*mV'
or'V=70*mV; Vt+=10*mV'
. Some standard functions are provided, see below. level
 How many levels up in the calling sequence to look for names in the namespace. Usually 0 for user code.
Standard functions for expressions:
rand()
 A uniform random number between 0 and 1.
randn()
 A Gaussian random number with mean 0 and standard deviation 1.
For example, these could be used to implement an adaptive model with random reset noise with the following string:
E = 1*mV V = Vr+rand()*5*mV

class
brian.
VariableReset
(resetvaluestate=1, state=0)¶ Resets specified state variable to the value of another state variable
Initialised with arguments:
resetvaluestate
 The state variable which contains the value to reset to.
state
 The name or number of the state variable to reset.
This will reset all of the neurons that have just spiked. The given state variable of the neuron group will be set to the value of the state variable
resetvaluestate
.

class
brian.
Refractoriness
(resetvalue=0.0 * volt, period=5.0 * msecond, state=0)¶ Holds the state variable at the reset value for a fixed time after a spike.
Initialised with arguments:
resetvalue
 The value to reset and hold to.
period
 The length of time to hold at the reset value. If using variable refractoriness, this is the maximum period.
state
 The name or number of the state variable to reset and hold.

class
brian.
SimpleCustomRefractoriness
(resetfun, period=5.0 * msecond, state=0)¶ Holds the state variable at the custom reset value for a fixed time after a spike.
Initialised as:
SimpleCustomRefractoriness(resetfunc[,period=5*ms[,state=0]])
with arguments:
resetfun
 The custom reset function
resetfun(P, spikes)
forP
aNeuronGroup
andspikes
a list of neurons that fired spikes. period
 The length of time to hold at the reset value.
state
 The name or number of the state variable to reset and hold, it is your responsibility to check that this corresponds to the custom reset function.
The assumption is that
resetfun(P, spikes)
will reset the state variablestate
on the groupP
for the spikes with indicesspikes
. The values assigned by the custom reset function are stored by this object, and they are clamped at these values forperiod
. This object does not introduce refractoriness for more than the one specified variablestate
or for spike indices other than those in the variablespikes
passed to the custom reset function.

class
brian.
CustomRefractoriness
(resetfun, period=5.0 * msecond, refracfunc=None)¶ Holds the state variable at the custom reset value for a fixed time after a spike.
Initialised as:
CustomRefractoriness(resetfunc[,period=5*ms[,refracfunc=resetfunc]])
with arguments:
resetfunc
 The custom reset function
resetfunc(P, spikes)
forP
aNeuronGroup
andspikes
a list of neurons that fired spikes. refracfunc
 The custom refractoriness function
refracfunc(P, indices)
forP
aNeuronGroup
andindices
a list of neurons that are in their refractory periods. In some cases, you can choose not to specify this, and it will use the reset function. period
 The length of time to hold at the reset value.

class
brian.
FunReset
(resetfun)¶ A reset with a userdefined function.
Initialised as:
FunReset(resetfun)
with argument:
resetfun
 A function
f(G,spikes)
whereG
is theNeuronGroup
andspikes
is an array of the indexes of the neurons to be reset.

class
brian.
NoReset
¶ Absence of reset mechanism.
Initialised as:
NoReset()
Thresholds¶
A threshold mechanism checks which neurons have fired a spike.

class
brian.
Threshold
(threshold=1.0 * mvolt, state=0)¶ All neurons with a specified state variable above a fixed value fire a spike.
Initialised as:
Threshold([threshold=1*mV[,state=0])
with arguments:
threshold
 The value above which a neuron will fire.
state
 The state variable which is checked.
Compilation
Note that if the global variable
useweave
is set toTrue
then this function will use aC++
accelerated version which runs approximately 3x faster.

class
brian.
StringThreshold
(expr, level=0)¶ A threshold specified by a string expression.
Initialised with arguments:
expr
 The expression used to test whether a neuron has fired a spike.
Should be a single statement that returns a value. For example,
'V>50*mV'
or'V>Vt'
. level
 How many levels up in the calling sequence to look for names in the namespace. Usually 0 for user code.

class
brian.
VariableThreshold
(threshold_state=1, state=0)¶ Threshold mechanism where one state variable is compared to another.
Initialised as:
VariableThreshold([threshold_state=1[,state=0]])
with arguments:
threshold_state
 The state holding the lower bound for spiking.
state
 The state that is checked.
If
x
is the value of state variablethreshold_state
on neuroni
andy
is the value of state variablestate
on neuroni
then neuroni
will fire ify>x
.Typically, using this class is more time efficient than writing a custom thresholding operation.
Compilation
Note that if the global variable
useweave
is set toTrue
then this function will use aC++
accelerated version.

class
brian.
EmpiricalThreshold
(threshold=1.0 * mvolt, refractory=1.0 * msecond, state=0, clock=None)¶ Empirical threshold, e.g. for HodgkinHuxley models.
In empirical models such as the HodgkinHuxley method, after a spike neurons are not instantaneously reset, but reset themselves as part of the dynamical equations defining their behaviour. This class can be used to model that. It is a simple threshold mechanism that checks e.g.
V>=Vt
but it only does so for neurons that haven’t recently fired (giving the dynamical equations time to reset the values naturally). It should be used in conjunction with theNoReset
object.Initialised as:
EmpiricalThreshold([threshold=1*mV[,refractory=1*ms[,state=0[,clock]]]])
with arguments:
threshold
 The lower bound for the state variable to induce a spike.
refractory
 The time to wait after a spike before checking for spikes again.
state
 The name or number of the state variable to check.
clock
 If this object is being used for a
NeuronGroup
which doesn’t use the default clock, you need to specify its clock here.

class
brian.
SimpleFunThreshold
(thresholdfun, state=0)¶ Threshold mechanism with a userspecified function.
Initialised as:
FunThreshold(thresholdfun[,state=0])
with arguments:
thresholdfun
 A function with one argument, the array of values for the specified state variable. For efficiency, this is a numpy array, and there is no unit checking.
state
 The name or number of the state variable to pass to the threshold function.
Sample usage:
FunThreshold(lambda V:V>=Vt,state='V')

class
brian.
FunThreshold
(thresholdfun)¶ Threshold mechanism with a userspecified function.
Initialised as:
FunThreshold(thresholdfun)
where
thresholdfun
is a function with one argument, the 2d state value array, where each row is an array of values for one state, of length N for N the number of neurons in the group. For efficiency, data are numpy arrays and there is no unit checking.Note: if you only need to consider one state variable, use the
SimpleFunThreshold
object instead.

class
brian.
NoThreshold
¶ No thresholding mechanism.
Initialised as:
NoThreshold()