### Applet: Spruce budworm model

Illustration of the dynamical system modeling an outbreak of the spruce budworm population. The evolution of the budworm population $w(t)$ is modeled by the autonomous differential equation $\diff{w}{t}=f(w)$, where \begin{align*} f(w)= r w \left(1 - \frac{w}{a}\right) - \frac{w^2}{1+w^2}. \end{align*} The left panel shows a plot of $f(w)$ (black curve), which changes depending on the value of the parameters $r$ and $b$ (changeable via sliders). If you click the play button in the lower left corner of one of the panels or increase $t$ manually via the red slider in the right panel, the evolution of $w(t)$ from the initial condition $w(t_0)=w_0$ is shown by the blue curves. In the left panel, $w(t)$ is a line on the horizontal axis. In the right panel, $w(t)$ is plotted versus time $t$. The direction of $w(t)$ can be determined by the sign of $f(w)$ or by turning on the vector field (with check box). Equilibria are displayed by circles in the left panel and horizontal lines in the right panel if you check the box.

Applet file: spruce_budworm_nondimensionalized.ggb

#### Applet links

This applet is found in the pages

#### General information about Geogebra Web applets

This applet was created using Geogebra. In most Geogebra applets, you can move objects by dragging them with the mouse. In some, you can enter values with the keyboard. To reset the applet to its original view, click the icon in the upper right hand corner.

You can download the applet onto your own computer so you can use it outside this web page or even modify it to improve it. You simply need to download the above applet file and download the Geogebra program onto your own computer.