1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
|
#!/usr/bin/env python
"""
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 brian2 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='v>1', reset='v=0', method='euler')
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 = S.it
plot((t % tau)/tau, neurons.a[i], ',')
xlabel('Spike phase')
ylabel('Parameter a')
show()
|
