# 阿利效应

## 数学模型

${\displaystyle {\frac {dN}{dt}}=rN\left({\frac {N}{A}}-1\right)\left(1-{\frac {N}{K}}\right),}$

${\displaystyle {\frac {dN}{dt}}=rN\left(1-{\frac {N}{K}}\right)}$

N = 种群规模；
r = 内禀增长率；
K = 环境承载力
A = 临界点；
dN/dt = 个体数增长率。

${\displaystyle {\frac {\partial N}{\partial t}}=D{\frac {\partial ^{2}N}{\partial x^{2}}}+rN\left({\frac {N}{A}}-1\right)\left(1-{\frac {N}{K}}\right),}$

D = 扩散系数
${\displaystyle {\frac {\partial ^{2}}{\partial x^{2}}}}$  = 一维拉普拉斯算子

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