Bifurcations

The bifurcations activity “Bifurcations” is designed to investigate changes in the long term behavior of solutions to autonomous differential equations. 

The activity displays three different views that are useful for examining the stability of equilibrium solutions.

• Slopefield: Users can add solutions to a slopefield for the equation y′ = f (y).

• Bifurcation Diagram: A plot of the equilibrium solutions versus the selected parameter a.

– Stable equilibria are located on the solid curve

– Unstable equilibria are located on the dashed curve.

– A vertical phase line with arrows indicates the stability for a single parameter value.

• Plot of y′versus y: The equilibrium points occur where the curve crosses the horizontal axis and the orange arrows indicate the stability of each.