{"type":"rich","version":"1.0","title":"Counting equilibria of the harvested logistic equation by the discriminant","html":"<span class=\"wb-embed wb-embed-math\" data-latex=\"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}\">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&lt;H_{c}=\\frac{rK}{4},\\ \\text{one if }H=H_{c},\\ \\text{none if }H&gt;H_{c}</span>","width":640,"height":320}