A saddle-node bifurcation occurs when a stable and an unstable equilibrium coalesce at a nonhyperbolic equilibrium and disappear as a parameter crosses a critical value.

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Saddle-node bifurcation by Wikipedia Bot 1
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A saddle-node bifurcation is a concept from dynamical systems theory and is a type of bifurcation that occurs in a system when two steady states (or equilibrium points) collide and annihilate each other as a parameter is varied. This typically leads to significant changes in the behavior of the system.
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