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.. currentmodule:: brian
.. index::
pair: example usage; plot
pair: example usage; run
pair: example usage; show
pair: example usage; yticks
pair: example usage; xlabel
pair: example usage; linspace
pair: example usage; ylabel
pair: example usage; SpikeMonitor
pair: example usage; NeuronGroup
.. _example-frompapers_Brette_2004:
Example: Brette_2004 (frompapers)
=================================
Phase locking in leaky integrate-and-fire model
-----------------------------------------------
Fig. 2A from:
Brette R (2004). Dynamics of one-dimensional spiking neuron models.
J Math Biol 48(1): 38-56.
This shows the phase-locking structure of a LIF driven by a sinusoidal
current. When the current crosses the threshold (a<3), the model
almost always phase locks (in a measure-theoretical sense).
::
from brian import *
#defaultclock.dt=0.01*ms # for a more precise picture
N=2000
tau=100*ms
freq=1/tau
eqs='''
dv/dt=(-v+a+2*sin(2*pi*t/tau))/tau : 1
a : 1
'''
neurons=NeuronGroup(N,eqs,threshold=1,reset=0)
neurons.a=linspace(2,4,N)
run(5*second,report='text') # discard the first spikes (wait for convergence)
S=SpikeMonitor(neurons)
run(5*second,report='text')
i,t=zip(*S.spikes)
plot((t % tau)/tau,i,'.')
xlabel('Spike phase')
ylabel('Parameter a')
yticks([0,N/2,N],[2,3,4])
show()
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