Information About

Period-doubling Bifurcation
  CATEGORIES ABOUT PERIOD-DOUBLING BIFURCATION
   
non-linear systems
   
bifurcation theory
   
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EXAMPLE


Consider the following logistical map for a modified Phillips Curve :

\pi_{t} = f(u_{t}) + a \pi_{t}^e

\pi_{t+1} = \pi_{t}^e + c (\pi_{t} - \pi_{t}^e)

f(u) = \beta_{1} + \beta_{2} e^{-u}

b > 0, 0 \leq c \leq 1, rac {df} {du} < 0


where \pi is the actual Inflation , \pi^e is the expected inflation, u is the level of unemployment, and m - \pi is the Money Supply growth rate. Keeping \beta_{1} = -2.5, \ \beta_{2} = 20, \ c = 0.75 and varying b, 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



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