Behavior of Equilibrium Points in Two-Dimensional Systems of Differential Equations

equilibrium behavior

supercritical Andronov-Hopf

This Demonstration illustrates the behavior of equilibrium points for various two-dimensional systems of differential equations. The solution curve for a specific initial condition is plotted in red over a stream plot of possible trajectories for the system.

Choose the type of behavior from the drop down menu and drag the Locator to choose the initial condition. The eigenvalues of the linearization of the system are shown at the top.

While this Demonstration does not offer an exhaustive list of all possible equilibrium point behaviors, it includes the most common and interesting of the two-dimensional cases.