Ideal equation |
Ideal equation |
|
0 |
0 |
\(\alpha\) |
0 |
\(\left[0,N\right]\) |
0 |
αP |
\(\left[0,1\right]\) |
Prey-dependent |
Type I |
αN |
αN |
0 |
\(\infty\) |
0 |
\(\infty\) |
0 |
\(\infty\) |
\(\left[\left.\ 0,\ \infty\right)\right.\ \) |
|
Type II |
\(\frac{\text{αN}}{N+b}\) |
\(\frac{\text{αN}}{N+b}\) |
0 |
\(\alpha\) |
0 |
\(\infty\) |
0 |
αP |
\(\left[\left.\ 0,\ \infty\right)\right.\ \) |
|
Type III |
\(\frac{\alpha N^{2}}{N^{2}+b}\) |
\(\frac{\alpha N^{2}}{N^{2}+b}\) |
0 |
\(\alpha\) |
0 |
\(\infty\) |
0 |
αP |
\(\left[\left.\ 0,\ \infty\right)\right.\ \) |
Ratio-dependent |
Type I |
\(\alpha\frac{N}{P}\) |
0 |
0 |
\(\infty\) |
αN |
αN |
0 |
\(\infty\) |
\(\left[\left.\ 0,\ \infty\right)\right.\ \) |
|
Type II |
\(\frac{\alpha\frac{N}{P}}{\frac{N}{P}+b}\) |
0 |
0 |
\(\alpha\) |
0 |
\(\frac{\text{αN}}{b}\) |
0 |
αP |
\(\left[\left.\ 0,\ \infty\right)\right.\ \) |
|
Type III |
\(\frac{\alpha\left(\frac{N}{P}\right)^{2}}{\left(\frac{N}{P}\right)^{2}+b}\) |
0 |
0 |
\(\alpha\) |
0 |
0 |
0 |
αP |
\(\left[\left.\ 0,\ \infty\right)\right.\ \) |
Beddington-DeAngelis |
Beddington-DeAngelis |
\(\frac{\text{αN}}{N+cP+b}\) |
0 |
0 |
\(\alpha\) |
0 |
\(\frac{\text{αN}}{c}\) |
0 |
αP |
\(\left[\left.\ 0,\ \infty\right)\right.\ \) |
Hassell-Varley |
Type I |
\(\alpha\left(\frac{N}{P^{m}}\right)\) |
\(\left\{\begin{matrix}\alpha N,\ \ \&m=0\\
0,\ \ \&m>0\\
\end{matrix}\right.\ \) |
0 |
\(\infty\) |
\(\left\{\begin{matrix}0,\ \ \&0\leq m<1\\
\alpha N,\ \ \&m=1\\
\end{matrix}\right.\ \) |
\(\left\{\begin{matrix}\infty,\ \ \&0\leq m<1\\
\alpha N,\ \ \&m=1\\
\end{matrix}\right.\ \) |
0 |
\(\infty\) |
\(\left[\left.\ 0,\ \infty\right)\right.\ \) |
|
Type II |
\(\frac{\alpha\left(\frac{N}{P^{m}}\right)}{\left(\frac{N}{P^{m}}\right)+b}\) |
\(\left\{\begin{matrix}\frac{\text{αN}}{N+b},\ \ \&m=0\\
0,\ \ \&m>0\\
\end{matrix}\right.\ \) |
0 |
\(\alpha\) |
0 |
\(\left\{\begin{matrix}\infty,\ \ \&0\leq m<1\\
\frac{\text{αN}}{b},\ \ \&m=1\\
\end{matrix}\right.\ \) |
0 |
αP |
\(\left[\left.\ 0,\ \infty\right)\right.\ \) |
|
Type III |
\(\frac{\alpha\left(\frac{N}{P^{m}}\right)^{2}}{\left(\frac{N}{P^{m}}\right)^{2}+b}\) |
\(\left\{\begin{matrix}\frac{\alpha N^{2}}{N^{2}+b},\ \ \&m=0\\
0,\ \ \&m>0\\
\end{matrix}\right.\ \) |
0 |
\(\alpha\) |
0 |
\(\left\{\begin{matrix}\infty,\ \ \&0\leq m<0.5\\
\frac{\alpha N^{2}}{b},\ \ \&m=0.5\\
0,\ \ \&0.5<m\leq 1\\
\end{matrix}\right.\ \) |
0 |
αP |
\(\left[\left.\ 0,\ \infty\right)\right.\ \) |
Kovai
|
Kovai
|
\[\alpha\left(1-e^{\frac{-Nu}{\left(\text{αP}\right)}}\right);\]
\[u=1-\left(\frac{b}{N}\right)\left(1-e^{\frac{-N}{b}}\right)\]
|
0
|
0
|
\[\alpha\]
|
0
|
\[Nu\in\left[0,N\right]\]
|
0
|
αP
|
\[\left[\left.\ 0,1\right)\right.\ \]
|