In mathematics, a period doubling bifurcation in a discrete dynamical system is a bifurcation in which the system switches to a new behavior with twice the period of the original system. That is, there exists two points such that applying the dynamics to each of the points yields the other point. Period doubling bifurcations can also occur in continuous dynamical systems, namely when a new limit cycle emerges from an existing limit cycle, and the period of the new limit cycle is twice that of the old one.
Consider the following logistical map for a modified Phillips curve:
- is the actual inflation
- is the expected inflation,
- u is the level of unemployment,
- is the money supply growth rate.
Keeping and varying , the system undergoes period doubling bifurcations, and after a point becomes chaotic, as illustrated in the bifurcation diagram on the right.
Period-halving bifurcation 
A period halving bifurcation in a dynamical system is a bifurcation in which the system switches to a new behavior with half the period of the original system. A series of period-halving bifurcations leads the system from chaos to order.
See also 
- Kuznetsov, Yuri A. (2004). Elements of Applied Bifurcation Theory. Applied Mathematical Sciences 112 (3rd ed.). Springer-Verlag. ISBN 0-387-21906-4. Zbl 1082.37002.
- The Flip (Period Doubling) Bifurcation in Discrete Time, Dynamic Processes