Hopf bifurcation
Critical point where a periodic solution arises
Hopf bifurcation
In the mathematics of dynamical systems and differential equations, a Hopf bifurcation is said to occur when varying a parameter of the system causes the set of solutions (trajectories) to change from being attracted to (or repelled by) a fixed point, and instead become attracted to (or repelled by) an oscillatory, periodic solution. The Hopf bifurcation is a two-dimensional analog of the pitchfork bifurcation. Many different kinds of systems exhibit Hopf bifurcations, from radio oscillators to railroad bogies. Trailers towed behind automobiles become infamously unstable if loaded incorrectly, or if designed with the wrong geometry. This offers an intuitive example of a Hopf bifurcation in the ordinary world, where stable motion becomes unstable and oscillatory as a parameter is varied. Fluid flows also exhibit Hopf bifurcation behavior when the transition from steady to unsteady laminar flow occurs. The general theory of how the solution sets of dynamical systems change in response to...
Read on Wikipedia · Image Hannes Vogel, CC BY-SA 4.0
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