50 / 60 : add x v plot using matplotlib.gridspec

help from Gemini

50_ode/60_Duffing_Oscillator.ipynb

@@ -196,8 +196,15 @@
     "    \n",
     "    t_out, x_out = ode_solver.rk4(slope, t_array, x_0)\n",
     "    x_out = np.array(x_out)\n",
-    "    _, axs = plt.subplots(2, 1, figsize=figsize)\n",
+    "    fig = plt.figure(figsize=figsize)\n",
+    "    gs = mg.GridSpec(2, 2, height_ratios=[1, 1], width_ratios=[1, 1])\n",
     "\n",
+    "    axs = (\n",
+    "        fig.add_subplot(gs[0, 0]),\n",
+    "        fig.add_subplot(gs[1, 0]),\n",
+    "        fig.add_subplot(gs[:, 1])\n",
+    "    )\n",
+    "    \n",
     "    for k in range(2):\n",
     "        axs[k].plot(t_out, x_out[:, k], label='Duffing')\n",
     "        axs[k].plot(t_out, x_out[:, k+2], label='Linear')\n",
@@ -206,6 +213,12 @@
     "    axs[0].set_ylabel('$x(t)$')\n",
     "    axs[1].set_ylabel(r'$\\frac{d}{dt}x(t)$')\n",
     "\n",
+    "    axs[2].plot(x_out[:, 0], x_out[:, 1], label='Duffing')\n",
+    "    axs[2].plot(x_out[:, 2], x_out[:, 3], label='Linear')\n",
+    "    axs[2].grid(True)\n",
+    "    axs[2].set_xlabel('$x(t)$')\n",
+    "    axs[2].set_ylabel(r'$\\frac{d}{dt}x(t)$')\n",
+    "\n",
     "    return axs\n",
     "\n"
    ]