Particle and Field Descriptions of Fluid Motion

Bifurcations: fixed points can be created/destroyed or their stability changes
Bifurcation points: parameter values at which these ↑ qualitative changes happen

Bifurcations provide models for transitions & instabilities as some control parameter is varied

This is a simple bifurcation diagram. From the figure, we can directly observe the meaning behind the term 'bifurcation'. The shape of the diagram resembles a pitchfork, hence it is called a 'pitchfork bifurcation'