Editing Bifurcation diagram (section)

== Applications ==
Consider a system of [[differential equation|differential equations]] that describes some physical quantity, that for concreteness could represent one of three examples: 1. the position and velocity of an undamped and frictionless pendulum, 2. a neuron's membrane potential over time, and 3. the average concentration of a virus in a patient's bloodstream. The differential equations for these examples include *parameters* that may affect the output of the equations. Changing the pendulum's length will affect its oscillation frequency, changing the magnitude of injected current into a neuron may transition the membrane potential from resting to spiking, and the long-term viral load in the bloodstream may decrease with carefully timed treatments. 

In general, researchers may seek to quantify how the long-term (asymptotic) behavior of a system of differential equations changes if a parameter is changed. In the [[dynamical systems]] branch of mathematics, a '''bifurcation diagram''' quantifies these changes by showing how fixed points, [[periodic orbit]]s, or [[chaos (mathematics)|chaotic]] [[attractor]]s of a system change as a function of [[Bifurcation theory|bifurcation parameter]]. Bifurcation diagrams are used to visualize these changes.