Загрузить файлы в «/»

educmm-lab3.ipynb

@@ -0,0 +1 @@
+{"metadata":{"kernelspec":{"language":"python","display_name":"Python 3","name":"python3"},"language_info":{"name":"python","version":"3.11.11","mimetype":"text/x-python","codemirror_mode":{"name":"ipython","version":3},"pygments_lexer":"ipython3","nbconvert_exporter":"python","file_extension":".py"},"kaggle":{"accelerator":"none","dataSources":[],"dockerImageVersionId":31012,"isInternetEnabled":true,"language":"python","sourceType":"notebook","isGpuEnabled":false}},"nbformat_minor":4,"nbformat":4,"cells":[{"cell_type":"code","source":"import numpy as np\nimport matplotlib.pyplot as plt","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2025-04-24T15:39:29.233558Z","iopub.execute_input":"2025-04-24T15:39:29.234789Z","iopub.status.idle":"2025-04-24T15:39:29.238658Z","shell.execute_reply.started":"2025-04-24T15:39:29.234760Z","shell.execute_reply":"2025-04-24T15:39:29.237725Z"}},"outputs":[],"execution_count":91},{"cell_type":"code","source":"alpha = 3 # CHANGE TO 4\nbeta = 0.002\ndelta = 0.0006\ngamma = 0.5\n\ndef lotka_volterra(x):\n    x_val, y_val = x\n    dx = alpha * x_val - beta * x_val * y_val\n    dy = delta * x_val * y_val - gamma * y_val\n    return np.array([dx, dy])","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2025-04-24T15:39:29.239977Z","iopub.execute_input":"2025-04-24T15:39:29.240291Z","iopub.status.idle":"2025-04-24T15:39:29.257620Z","shell.execute_reply.started":"2025-04-24T15:39:29.240259Z","shell.execute_reply":"2025-04-24T15:39:29.256637Z"}},"outputs":[],"execution_count":92},{"cell_type":"code","source":"def rk4(x_0, t_n, f, h):\n    steps = int(t_n / h)\n    x = np.linspace(0, 100, steps)\n    y = np.linspace(0, 100, steps)\n    u_i = x_0\n    i = 0\n    for i in range(steps):\n        k1 = h * f(u_i)\n        k2 = h * f(u_i + 0.5 * k1)\n        k3 = h * f(u_i + 0.5 * k2)\n        k4 = h * f(u_i + k3)\n        \n        u_n = u_i + (1 / 6) * (k1 + k2 + k3 + k4)\n        \n        x[i] = u_n[0]\n        y[i] = u_n[1]\n        \n        u_i = u_n\n    return (x, y)","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2025-04-24T15:48:19.224365Z","iopub.execute_input":"2025-04-24T15:48:19.224630Z","iopub.status.idle":"2025-04-24T15:48:19.231102Z","shell.execute_reply.started":"2025-04-24T15:48:19.224611Z","shell.execute_reply":"2025-04-24T15:48:19.230195Z"}},"outputs":[],"execution_count":114},{"cell_type":"code","source":"tn = 10\nh = 0.01\n\ntrajectories = []\nfor i in range(1, 11):\n    for j in range(1, 11):\n        x0 = [200 * i, 200 * j]\n        traj = rk4(x0, tn, lotka_volterra, h)\n        trajectories.append(traj)\n\n# Вывод сообщения о завершении\nprint(f\"Рассчитано {len(trajectories)} траекторий.\")","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2025-04-24T15:48:39.470329Z","iopub.execute_input":"2025-04-24T15:48:39.470921Z","iopub.status.idle":"2025-04-24T15:48:41.911947Z","shell.execute_reply.started":"2025-04-24T15:48:39.470895Z","shell.execute_reply":"2025-04-24T15:48:41.911028Z"}},"outputs":[{"name":"stdout","text":"Рассчитано 100 траекторий.\n","output_type":"stream"}],"execution_count":116},{"cell_type":"code","source":"plt.figure(figsize=(10, 6))\nfor traj in trajectories:\n    plt.plot(traj[:, 0], traj[:, 1], linewidth=0.5)\nplt.xlabel(\"Жертвы (x)\")\nplt.ylabel(\"Хищники (y)\")\nplt.title(\"Фазовый портрет модели Лотки–Вольтерры\")\nplt.grid()\nplt.show()","metadata":{"trusted":true,"execution":{"iopub.status.busy":"2025-04-24T15:42:01.176494Z","iopub.execute_input":"2025-04-24T15:42:01.176788Z","iopub.status.idle":"2025-04-24T15:42:01.483172Z","shell.execute_reply.started":"2025-04-24T15:42:01.176769Z","shell.execute_reply":"2025-04-24T15:42:01.482311Z"}},"outputs":[{"output_type":"display_data","data":{"text/plain":"<Figure size 1000x600 with 1 Axes>","image/png":"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 truncated