Chapter 3

Visualizing the dynamic perspectives of first-order ODE's.

Visualizing the logistic model.

Here we visualize the solutions to the logistic model

\begin{align} \dfrac{dy}{dt} = ry\Big(1- \dfrac{y}{K}\Big), \end{align}

with constants $r,K > 0$.

The figure below shows the solution curves $y(t)$ for various values of $y(0) \ge 0$.

To play with the visulization yourself, choose values for the constants $r$, $K$, and choose the intial condition $y(0)=y_0$ at time $t=0$: