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无编辑摘要
=== Prey 猎物 ===
=== 猎物 ===
When multiplied out, the prey equation becomes
When multiplied out, the prey equation becomes
=== Predators 捕食者===
=== 捕食者===
The predator equation becomes
The predator equation becomes
=== A simple example 简单示例 ===
=== 简单示例 ===
[[文件:WeChat Screenshot 20210111180355.png|缩略图|右|前文提到关于狒狒和猎豹问题的种群动态。]]
[[文件:WeChat Screenshot 20210111180355.png|缩略图|右|前文提到关于狒狒和猎豹问题的种群动态。]]
=== Phase-space plot of a further example 相空间图的进一步示例 ===
=== 相空间图的进一步示例 ===
[[文件:WeChat Screenshot 20210112125549.png|缩略图|左|捕猎相空间图]]
[[文件:WeChat Screenshot 20210112125549.png|缩略图|左|捕猎相空间图]]
{{mvar|α}} = 2/3, {{mvar|β}} = 4/3, {{mvar|γ}} = 1 = {{mvar|δ}}. 假设{{math|''x'', ''y''}}处于“千”级别还不到“万“。圆圈代表从{{mvar|x}} = {{mvar|y}} = 0.9 到 1.8时猎物和捕食者的初始条件，步长为0.1，不动点为（1，1/2）。
{{mvar|α}} = 2/3, {{mvar|β}} = 4/3, {{mvar|γ}} = 1 = {{mvar|δ}}. 假设{{math|''x'', ''y''}}处于“千”级别还不到“万“。圆圈代表从{{mvar|x}} = {{mvar|y}} = 0.9 到 1.8时猎物和捕食者的初始条件，步长为0.1，不动点为（1，1/2）。
== Dynamics of the system 系统动力学 ==
== 系统动力学 ==
In the model system, the predators thrive when there are plentiful prey but, ultimately, outstrip their food supply and decline. As the predator population is low, the prey population will increase again. These dynamics continue in a cycle of growth and decline.
In the model system, the predators thrive when there are plentiful prey but, ultimately, outstrip their food supply and decline. As the predator population is low, the prey population will increase again. These dynamics continue in a cycle of growth and decline.
=== Population equilibrium 种群平衡===
=== 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:
=== Stability of the fixed points 不动点的稳定性 ===
=== 不动点的稳定性 ===
The stability of the fixed point at the origin can be determined by performing a [[linearization]] using [[partial derivative]]s.
The stability of the fixed point at the origin can be determined by performing a [[linearization]] using [[partial derivative]]s.
====First fixed point (extinction) 第一不动点（灭绝）====
====第一不动点（灭绝）====
====Second fixed point (oscillations) 第二不动点（震荡）====
====第二不动点（震荡）====