Counting equilibria of the harvested logistic equation by the discriminant (Q1678): Difference between revisions
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| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
| Property / LaTeX source | |||
| Property / LaTeX source: rN\\Bigl(1-\\frac{N}{K}\\Bigr)-H=0\\ \\iff\\ \\frac{r}{K}N^{2}-rN+H=0;\\qquad \\Delta=r^{2}-\\frac{4rH}{K}\\ \\Rightarrow\\ \\text{two equilibria if }H<H_{c}=\\frac{rK}{4},\\ \\text{one if }H=H_{c},\\ \\text{none if }H>H_{c} / rank | |||
| Property / instance of | |||
| Property / instance of: mathematical expression / rank | |||
Normal rank | |||
| Property / LaTeX source | |||
rN\\Bigl(1-\\frac{N}{K}\\Bigr)-H=0\\ \\iff\\ \\frac{r}{K}N^{2}-rN+H=0;\\qquad \\Delta=r^{2}-\\frac{4rH}{K}\\ \\Rightarrow\\ \\text{two equilibria if }H<H_{c}=\\frac{rK}{4},\\ \\text{one if }H=H_{c},\\ \\text{none if }H>H_{c} | |||
| Property / LaTeX source: rN\\Bigl(1-\\frac{N}{K}\\Bigr)-H=0\\ \\iff\\ \\frac{r}{K}N^{2}-rN+H=0;\\qquad \\Delta=r^{2}-\\frac{4rH}{K}\\ \\Rightarrow\\ \\text{two equilibria if }H<H_{c}=\\frac{rK}{4},\\ \\text{one if }H=H_{c},\\ \\text{none if }H>H_{c} / rank | |||
Normal rank | |||
Latest revision as of 07:28, 4 September 2026
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Counting equilibria of the harvested logistic equation by the discriminant |
No description defined |
Statements
rN\\Bigl(1-\\frac{N}{K}\\Bigr)-H=0\\ \\iff\\ \\frac{r}{K}N^{2}-rN+H=0;\\qquad \\Delta=r^{2}-\\frac{4rH}{K}\\ \\Rightarrow\\ \\text{two equilibria if }H<H_{c}=\\frac{rK}{4},\\ \\text{one if }H=H_{c},\\ \\text{none if }H>H_{c}
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