961
个编辑
更改
跳到导航
跳到搜索
第290行：
第290行： − + 第296行：
第296行： − 人口均衡发生在模型中，当两个人口水平都没有变化时，即。当两个导数都等于0时:+ + − − <math>x(\alpha - \beta y) = 0,</math> − − X (alpha-beta y) = 0 − − <math>-y(\gamma - \delta x) = 0.</math> − − < math >-y (gamma-delta x) = 0 </math > − 第316行：
第308行： − 上述方程组得出两个解:+ − − − <math>\{y = 0,\ \ x = 0\}</math> − − { y = 0，x = 0} − − − and − − − <math>\left\{y = \frac{\alpha}{\beta},\ \ x = \frac{\gamma}{\delta} \right\}.</math> − − 左{ y = frac { alpha }{ beta } ，x = frac { gamma }{ delta }右} − 第348行：
第326行： − 因此，有两个均衡。+ 第356行：
第334行： − 第一个解决方案有效地代表了这两个物种的灭绝。如果两个种群都是0，那么它们将无限期地保持这种状态。第二个解表示一个固定点，在这个点上，两个种群都维持它们当前的非零数，并且在简化模型中，无限期地维持这个数。达到这种平衡的总体水平取决于参数 α，β，γ 和 δ 的选择值。+ − −
→Population equilibrium
===Population equilibrium===
=== Population equilibrium 种群平衡===
Population equilibrium occurs in the model when neither of the population levels is changing, i.e. when both of the derivatives are equal to 0:
Population equilibrium occurs in the model when neither of the population levels is changing, i.e. when both of the derivatives are equal to 0:
Population equilibrium occurs in the model when neither of the population levels is changing, i.e. when both of the derivatives are equal to 0:
Population equilibrium occurs in the model when neither of the population levels is changing, i.e. when both of the derivatives are equal to 0:
当捕猎双方种群数量都没有变化时，即当式中两个导数都等于0时，模型就会出现种群平衡：
:<math>x(\alpha - \beta y) = 0,</math>
:<math>x(\alpha - \beta y) = 0,</math>
:<math>-y(\gamma - \delta x) = 0.</math>
:<math>-y(\gamma - \delta x) = 0.</math>
The above system of equations yields two solutions:
The above system of equations yields two solutions:
对上面的方程组进行求解，得到：
:<math>\{y = 0,\ \ x = 0\}</math>
:<math>\{y = 0,\ \ x = 0\}</math>
and
and
及
及
:<math>\left\{y = \frac{\alpha}{\beta},\ \ x = \frac{\gamma}{\delta} \right\}.</math>
:<math>\left\{y = \frac{\alpha}{\beta},\ \ x = \frac{\gamma}{\delta} \right\}.</math>
Hence, there are two equilibria.
Hence, there are two equilibria.
因此我们得到了两个平衡点（对应于上式的两个解）。
The first solution effectively represents the extinction of both species. If both populations are at 0, then they will continue to be so indefinitely. The second solution represents a fixed point at which both populations sustain their current, non-zero numbers, and, in the simplified model, do so indefinitely. The levels of population at which this equilibrium is achieved depend on the chosen values of the parameters α, β, γ, and δ.
The first solution effectively represents the extinction of both species. If both populations are at 0, then they will continue to be so indefinitely. The second solution represents a fixed point at which both populations sustain their current, non-zero numbers, and, in the simplified model, do so indefinitely. The levels of population at which this equilibrium is achieved depend on the chosen values of the parameters α, β, γ, and δ.
第一种解明显代表了两种物种的灭绝。当它们的解都为0时，它们将继续无限期地保持绝种状态。第二种解则表示两个种群都维持其当前固定数量（非零点），在简化模型中，它们无限期地保持状态不变。达到此平衡的总体水平取决于参数''α'', ''β'', ''γ'', 和 ''δ''的选定值。
===Stability of the fixed points===
===Stability of the fixed points===