.. currentmodule:: brian2

.. Izhikevich_2003:

Example: Izhikevich_2003
========================


        .. only:: html

            .. |launchbinder| image:: http://mybinder.org/badge.svg
            .. _launchbinder: https://mybinder.org/v2/gh/brian-team/brian2-binder/master?filepath=examples/frompapers/Izhikevich_2003.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|_

        

Fig. 3 of

Simple Model of Spiking Neurons
IEEE Transactions on Neural Networks ( Volume: 14, Issue: 6, Nov. 2003)
Eugene M. Izhikevich

based on net.m by Eugene M. Izhikevich (http://izhikevich.org/publications/spikes.htm)

Akif Erdem Sağtekin and Sebastian Schmitt, 2022

::

    import matplotlib.pyplot as plt
    import numpy as np
    
    from brian2 import NeuronGroup, Synapses, SpikeMonitor, StateMonitor
    from brian2 import ms, mV
    from brian2 import defaultclock, run
    
    tfinal = 1000 * ms
    Ne = 800
    Ni = 200
    
    re = np.random.uniform(size=Ne)
    ri = np.random.uniform(size=Ni)
    weights = np.hstack(
        [
            0.5 * np.random.uniform(size=(Ne + Ni, Ne)),
            -np.random.uniform(size=(Ne + Ni, Ni)),
        ]
    ).T
    
    defaultclock.dt = 1 * ms
    
    eqs = """dv/dt = (0.04*v**2 + 5*v + 140 - u + I + I_noise )/ms : 1
             du/dt = (a*(b*v - u))/ms  : 1
             I : 1
             I_noise : 1
             a : 1
             b : 1
             c : 1
             d : 1
           """
    
    N = NeuronGroup(Ne + Ni, eqs, threshold="v>=30", reset="v=c; u+=d", method="euler")
    N.v = -65
    
    N_exc = N[:Ne]
    N_inh = N[Ne:]
    
    spikemon = SpikeMonitor(N)
    statemon = StateMonitor(N, 'v', record=0, when='after_thresholds')
    N_exc.a = 0.02
    N_exc.b = 0.2
    N_exc.c = -65 + 15 * re**2
    N_exc.d = 8 - 6 * re**2
    
    N_inh.a = 0.02 + 0.08 * ri
    N_inh.b = 0.25 - 0.05 * ri
    N_inh.c = -65
    N_inh.d = 2
    
    N_exc.u = "b*v"
    N_inh.u = "b*v"
    
    S = Synapses(
        N,
        N,
        "w : 1",
        on_pre={"up": "I += w", "down": "I -= w"},
        delay={"up": 0 * ms, "down": 1 * ms},
    )
    S.connect()
    S.w[:] = weights.flatten()
    
    N_exc.run_regularly("I_noise = 5*randn()", dt=1 * ms)
    N_inh.run_regularly("I_noise = 2*randn()", dt=1 * ms)
    
    run(tfinal)
    
    fig, (ax, ax_voltage) = plt.subplots(2, 1, sharex=True,
                                         gridspec_kw={'height_ratios': (3, 1)})
    
    ax.scatter(spikemon.t / ms, spikemon.i[:], marker="_", color="k", s=10)
    ax.set_xlim(0, tfinal / ms)
    ax.set_ylim(0, len(N))
    ax.set_ylabel("neuron number")
    ax.set_yticks(np.arange(0, len(N), 100))
    ax.spines['right'].set_visible(False)
    ax.spines['top'].set_visible(False)
    ax.axhline(Ne, color="k")
    ax.text(500, 900, 'inhibitory', backgroundcolor='w', color='k', ha='center')
    ax.text(500, 400, 'excitatory', backgroundcolor='w', color='k', ha='center')
    
    ax_voltage.plot(statemon.t / ms, np.clip(statemon.v[0], -np.inf, 30),
                   color='k')
    ax_voltage.text(25, 0, 'v₁(t)')
    ax_voltage.set_xticks(np.arange(0, tfinal / ms, 100))
    ax_voltage.spines['right'].set_visible(False)
    ax_voltage.spines['top'].set_visible(False)
    ax_voltage.set_xlabel("time, ms")
    
    plt.show()
    

.. image:: ../resources/examples_images/frompapers.Izhikevich_2003.1.png