import numpy as np
import matplotlib.pyplot as plt
from brian2 import *

# Define the Lorenz96 system
def lorenz96(X, t):
    """ The Lorenz 96 system """
    N = len(X)
    dxdt = np.zeros(N)
    for i in range(N):
        dxdt[i] = (X[(i+1)%N] - X[i-2]) * X[i-1] - X[i] + 8.17
    return dxdt

# Set the parameters
N = 100  # number of neurons
tau = 10*ms  # membrane time constant
tau_p = 20*ms  # STDP potentiation time constant
tau_n = 20*ms  # STDP depression time constant
w_min = 0  # minimum synaptic weight
w_max = 1  # maximum synaptic weight
alpha = 0.01  # regularization coefficient for readout weights
beta = 0.001  # learning rate for readout weights
T = 10000*ms  # simulation time
dt = 1*ms  # simulation time step
t_train = 8000*ms  # training time
t_test = 2000*ms  # testing time

# Define the spiking neuron model
eqs_neuron = '''
dv/dt = (-v + I)/tau : 1 (unless refractory)
I : 1
spike_times : second
'''

# Define the STDP synapse model
eqs_synapse = '''
w : 1
x_pre : 1
x_post : 1
'''
eqs_synapse_pre = '''
x_pre = 1
w = clip(w + alpha * x_post, w_min, w_max)
'''
eqs_synapse_post = '''
x_post = 1
w = clip(w - beta * x_pre, w_min, w_max)
'''

# Define the spiking neural network model
net = Network()
G = NeuronGroup(N, eqs_neuron, threshold='v>=1', reset='v=0', refractory=5*ms)
G.I = 0
net.add(G)

S = Synapses(G, G, eqs_synapse, on_pre=eqs_synapse_pre, on_post=eqs_synapse_post)
S.connect(condition='i!=j')
S.w = 'rand() * (w_max - w_min) + w_min'
net.add(S)

# Define the readout layer model
N_readout = 20  # number of readout neurons
eqs_readout = '''
dv/dt = (-v + I)/tau : 1 (unless refractory)
I = dot(w, R.v) : 1
spike_times : second
'''
R = NeuronGroup(N_readout, eqs_readout, threshold='v>=1', reset='v=0', refractory=5*ms)
R.spike_times = [0]*N_readout
net.add(R)

W_readout = np.random.randn(N, N_readout) * 0.01
for i in range(N_readout):
    net.connect(G, R[i], weight=W_readout[:,i])

# Set up the monitors
mon_G = SpikeMonitor(G)
mon_R = SpikeMonitor(R)

# Run the simulation
net.run(T)

# Extract the spikes
t_spikes_G = np.array(mon_G.t/ms)
i_sp
