Question

does the pair of equilibria produced by a saddle-node bifurcation have to consist of one that is stable and one that is unstable?

Answer 1

This bifurcation is called a saddle-node bifurcation. In it, a pair of hyperbolic equilibria, one stable and one unstable, coalesce at the bifurcation point, annihilate each other and disappear.

What is a bifurcation equilibria?

• The mathematical study of changes in a family of curves' qualitative or topological structure, such as the integral curves of a family of vector fields or the solutions to a family of differential equations, is known as bifurcation theory.
• A bifurcation happens when a tiny, gradual change in a system's parameter values (the bifurcation parameters) results in an abrupt, "qualitative," or topological change in the system's behavior.
• This term is most frequently used to refer to the mathematical study of dynamical systems.
• Both continuous systems (represented by ordinary, delay, or partial differential equations) and discrete systems can experience bifurcations (described by maps).

To learn more about bifurcation equilibria, refer to

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