.. currentmodule:: brian2

.. Sturzl_et_al_2000:

Example: Sturzl_et_al_2000
==========================


        .. only:: html

            .. |launchbinder| image:: file:///usr/share/doc/python-brian-doc/docs/badge.svg
            .. _launchbinder: https://mybinder.org/v2/gh/brian-team/brian2-binder/master?filepath=examples/frompapers/Sturzl_et_al_2000.ipynb

            .. note::
               You can launch an interactive, editable version of this
               example without installing any local files
               using the Binder service (although note that at some times this
               may be slow or fail to open): |launchbinder|_

        

Adapted from
Theory of Arachnid Prey Localization
W. Sturzl, R. Kempter, and J. L. van Hemmen
PRL 2000

Poisson inputs are replaced by integrate-and-fire neurons

Romain Brette

::

    from brian2 import *
    
    # Parameters
    degree = 2 * pi / 360.
    duration = 500*ms
    R = 2.5*cm  # radius of scorpion
    vr = 50*meter/second  # Rayleigh wave speed
    phi = 144*degree  # angle of prey
    A = 250*Hz
    deltaI = .7*ms  # inhibitory delay
    gamma = (22.5 + 45 * arange(8)) * degree  # leg angle
    delay = R / vr * (1 - cos(phi - gamma))   # wave delay
    
    # Wave (vector w)
    time = arange(int(duration / defaultclock.dt) + 1) * defaultclock.dt
    Dtot = 0.
    w = 0.
    for f in arange(150, 451)*Hz:
        D = exp(-(f/Hz - 300) ** 2 / (2 * (50 ** 2)))
        rand_angle = 2 * pi * rand()
        w += 100 * D * cos(2 * pi * f * time + rand_angle)
        Dtot += D
    w = .01 * w / Dtot
    
    # Rates from the wave
    rates = TimedArray(w, dt=defaultclock.dt)
    
    # Leg mechanical receptors
    tau_legs = 1 * ms
    sigma = .01
    eqs_legs = """
    dv/dt = (1 + rates(t - d) - v)/tau_legs + sigma*(2./tau_legs)**.5*xi:1
    d : second
    """
    legs = NeuronGroup(8, model=eqs_legs, threshold='v > 1', reset='v = 0',
                       refractory=1*ms, method='euler')
    legs.d = delay
    spikes_legs = SpikeMonitor(legs)
    
    # Command neurons
    tau = 1 * ms
    taus = 1.001 * ms
    wex = 7
    winh = -2
    eqs_neuron = '''
    dv/dt = (x - v)/tau : 1
    dx/dt = (y - x)/taus : 1 # alpha currents
    dy/dt = -y/taus : 1
    '''
    neurons = NeuronGroup(8, model=eqs_neuron, threshold='v>1', reset='v=0',
                          method='exact')
    synapses_ex = Synapses(legs, neurons, on_pre='y+=wex')
    synapses_ex.connect(j='i')
    synapses_inh = Synapses(legs, neurons, on_pre='y+=winh', delay=deltaI)
    synapses_inh.connect('abs(((j - i) % N_post) - N_post/2) <= 1')
    spikes = SpikeMonitor(neurons)
    
    run(duration, report='text')
    
    nspikes = spikes.count
    phi_est = imag(log(sum(nspikes * exp(gamma * 1j))))
    print("True angle (deg): %.2f" % (phi/degree))
    print("Estimated angle (deg): %.2f" % (phi_est/degree))
    rmax = amax(nspikes)/duration/Hz
    polar(concatenate((gamma, [gamma[0] + 2 * pi])),
          concatenate((nspikes, [nspikes[0]])) / duration / Hz,
          c='k')
    axvline(phi, ls='-', c='g')
    axvline(phi_est, ls='-', c='b')
    show()
    

