In dynamical systems theory, a period-doubling bifurcation occurs when a slight change in a system's parameters causes a new periodic trajectory to emerge from an existing periodic trajectory—the new one having double the period of the original. With the doubled period, it takes twice as long (or, in a discrete dynamical system, twice as many iterations) for the numerical values visited by the system to repeat themselves.
A period-halving bifurcation occurs when a system switches to a new behavior with half the period of the original system.
A period-doubling cascade is an infinite sequence of period-doubling bifurcations. Such cascades are a common route by which dynamical systems develop chaos.[1] In hydrodynamics, they are one of the possible routes to turbulence.[2]
- ^ Alligood (1996) et al., p. 532
- ^ Thorne, Kip S.; Blandford, Roger D. (2017). Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics. Princeton University Press. pp. 825–834. ISBN 9780691159027.