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Definition: For an equation of the form dy/dt = f(a,y), where a is a real parameter, the critical points (equilibrium solutions) usually depend on the value of a. As a steadily increases or decreases, it often happens that at a certain value of a, called a bifurcation point, critical points come together, or separate, and equilibrium solutions may either be lost or gained.
Source: Elementary Differential Equations and Boundary Value Problems - William Boyce & Richard DiPrima