Lotka–Volterra 捕食者-猎物模型动态模拟器

POST http://127.0.0.1:3003/zh/api/tools/lotka-volterra-predator-prey

{
  "mcpServers": {
    "elysiatools-lotka-volterra-predator-prey": {
      "name": "lotka-volterra-predator-prey",
      "description": "求解并可视化经典 Lotka–Volterra 捕食者-猎口方程组 dN/dt = rN − aNP、dP/dt = bNP − mP：RK4 数值积分（6000 步，带 Hamilton 守恒量 V = bN − m·ln N + aP − r·ln P 漂移监控），输出猎物/捕食者相位振荡的时间序列曲线与闭合轨道相平面图（含共存平衡点 N*=m/b、P*=r/a 与线性化周期 T ≈ 2π/√(rm)）。自动检测周期数量与实测周期、种群振幅范围，并说明中性振荡的结构不稳定性——周期振幅完全由初始条件决定，真实系统会因密度依赖而阻尼或因富集悖论而自激。",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=lotka-volterra-predator-prey",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "lotka-volterra-predator-prey",
    "arguments": {
  "rPrey": 0.5,
  "aPred": 0.01,
  "bConv": 0.01,
  "mPred": 0.4,
  "n0": 60,
  "p0": 30,
  "tMax": 60
}
  }
}