System of Linear DEs Real Distinct Eigenvalues #2
- Erik Jacobsen
- Differential Equation
Shown below is the phase portrait for a linear system of differential equations with constant coefficients and two real, distinct eigenvalues. Here, the derivatives are with respect to time, and we are interested in the behavior of the solutions to the differential equation as time increases from zero. Each solution to the differential equation is called a trajectory. The initial values (at t = 0) of each solution are shown as points (red dots) in the phase plane (the xy-plane).
Try dragging the initial value points closer to and further from the eigenvectors (shown as green lines). Do the solutions move toward the origin or away from it? Why do you think the origin is called an unstable saddle in this phase portrait?