Exploring Stability, Bifurcations, and the Road to Chaos
Bifurcations are qualitative changes in the behavior of a system as a control parameter is varied. They are critical points where the number or stability of fixed points (or periodic orbits) changes.
The spontaneous creation or annihilation of a pair of fixed points (one stable, one unstable).
Also known as Tangent Bifurcation.
A stable fixed point becomes unstable and a new stable period-2 cycle (or orbit) is born.
The main route to chaos in discrete systems.
A fixed point loses stability and an isolated periodic orbit (a limit cycle) is born.
The transition from a stable point to a stable oscillation.