I take it no one is familiar with Dif EQ? I had 3 dif posts with no responses, meh! Well, those were the hardest of my assignment so I guess they were tough to answer.
Determine a mathematical model that has 3 first-order differential equations for the paragraph below. Use the following:
x(t) is the population of a predator
y(t) and z(t) are the populations of 2 animals that are the predator's prey
"We know the predator population grows from eating its prey (the 2 animals). Also, it does not have any enemies. Hence, it only declines as a result of natural deaths. Also, if there were not predator, the prey population would grow at an exponential rate. Further, if there were not predator, we know that the prey population would grow at a logistic rate"
I'd appreciate if someone could look this over for me to see if it makes sense. I put a lot of time into coming up w/ this result.
expnentially
\begin{eqnarray*}
\frac{dx(t)}{dt} &=& -ax(t)+bx(t)y(t)+cx(t)z(t) \\
\frac{dy(t)}{dt} &=& dy(t)-ex(t)y(t)-hy(t)z(t) \\
\frac{dz(t)}{dt} &=& fz(t)-gx(t)z(t)-kz(t)y(t)
\end{eqnarray*}
logistically
\begin{eqnarray*}
\frac{dx(t)}{dt} &=& -ax(t)+bx(t)y(t)+cx(t)z(t) \\
\frac{dy(t)}{dt} &=& d_{1}y(t)-ex(t)y(t)-h_{1}y(t)^{2} \\
\frac{dz(t)}{dt} &=& d_{2}z(t)-gx(t)z(t)-h_{2}z(t)^{2}
\end{eqnarray*}
EDIT: get LaTeX error so I just included in the code w/ out the [math ]stuff. Not sure why it was giving an error.