import numpy as np
import matplotlib.pyplot as plt

# 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

# Define the spiking neuron model
class Neuron:
    def __init__(self, tau, I=0.0):
        self.tau = tau
        self.I = I
        self.v = 0.0
        self.spike_times = []
    
    def update(self, dt, I=0.0):
        dvdt = (-self.v + self.I + I) / self.tau
        self.v += dvdt * dt
        if self.v >= 1.0:
            self.v = 0.0
            self.spike_times.append(dt)

# Define the STDP synapse model
class Synapse:
    def __init__(self, tau_p, tau_n, w_min, w_max):
        self.tau_p = tau_p
        self.tau_n = tau_n
        self.w_min = w_min
        self.w_max = w_max
        self.w = 0.0
        self.x_pre = 0.0
        self.x_post = 0.0
    
    def update(self, dt, pre_spike, post_spike):
        dwdt = 0.0
        if pre_spike:
            self.x_pre = 1.0
        else:
            self.x_pre = np.exp(-dt / self.tau_p) * self.x_pre
        
        if post_spike:
            self.x_post = 1.0
        else:
            self.x_post = np.exp(-dt / self.tau_n) * self.x_post
        
        dwdt = self.x_pre * self.x_post
        self.w += dwdt * dt
        self.w = np.clip(self.w, self.w_min, self.w_max)

# Define the spiking neural network model
class SNN:
    def __init__(self, N, tau, tau_p, tau_n, w_min, w_max, alpha, beta):
        self.N = N
        self.tau = tau
        self.tau_p = tau_p
        self.tau_n = tau_n
        self.w_min = w_min
        self.w_max = w_max
        self.alpha = alpha
        self.beta = beta
        self.neurons = [Neuron(tau) for i in range(N)]
        self.synapses = np.zeros((N,N), dtype=object)
        for i in range(N):
            for j in range(N):
                self.synapses[i,j] = Synapse(tau_p, tau_n, w_min, w_max)
        self.readout_weights = np.random.randn(N) * 0.01
    
    def train(self, X_train, y_train, learning_rate, num_epochs):
        for epoch in range(num_epochs):
            for i in range(len(X_train)):
                # Reset neurons and synapses
                for j in range(self.N):
                    self.neurons[j].v = 0.0
                    self.neurons[j].spike_times = []
                    for k in range(self.N):
                        self.synapses[j,k
