Chapter 11, Exploration 44

The tool below models a predator-prey system. Use it to answer the following questions. The point that indicates the initial condition is labelled \(A\) and is colored red.

• Move the point \(A\) around to choose a variety of initial conditions and describe what you see. In particular, how would you characterize the fixed point at \((\frac{2}{15}, \frac{22}{15})\) using the terminology of theorem 11.2?
• Choose an initial conditions near the fixed point at \((\frac{1}{2},0)\) and describe these orbits. How would you characterize the fixed point at \((\frac{1}{2},0)\) using the terminology of theorem 11.2?
• Choose an initial conditions very near the \(y\)-axis (especially with \(y \leq \frac{1}{2}\)) and describe these orbits. How would you characterize the fixed point at (0,0) using the terminology of theorem 11.2?