Lotka–Volterra 种间竞争模型模拟器

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

{
  "mcpServers": {
    "elysiatools-lotka-volterra-competition": {
      "name": "lotka-volterra-competition",
      "description": "求解并可视化 Lotka–Volterra 种间竞争方程组 dN₁/dt = r₁N₁(1−(N₁+α₁₂N₂)/K₁)、dN₂/dt = r₂N₂(1−(N₂+α₂₁N₁)/K₂)：RK4 数值积分（6000 步）输出双物种 N(t) 时间序列曲线与带零增长等斜线的 N₁–N₂ 相平面轨迹。按等斜线几何自动判定四种经典结局——稳定共存（种间竞争均弱于种内）、物种 1/2 竞争排斥、双稳态优先效应——给出共存平衡点 N₁*=(K₁−α₁₂K₂)/(1−α₁₂α₂₁)、N₂*=(K₂−α₂₁K₁)/(1−α₁₂α₂₁)、终态种群与灭绝判定。支持边界情况（某物种初始为 0）。",
      "baseUrl": "http://127.0.0.1:3003/mcp/sse?toolId=lotka-volterra-competition",
      "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-competition",
    "arguments": {
  "r1": 0.5,
  "r2": 0.4,
  "k1": 100,
  "k2": 80,
  "alpha12": 0.6,
  "alpha21": 0.5,
  "n10": 10,
  "n20": 8,
  "tMax": 60
}
  }
}