PERIOD-DOUBLING BIFURCATION

In mathematics, a 'Period doubling bifurcation' in a dynamical system is a bifurcation in which the system switches to a new behavior with twice the period of the original system. The hallmark of this is a Floquet multiplier of -1.

Contents

Example

Period-halving bifurcation

See also

External links

Example

Consider the following logistical map for a modified Phillips curve:
$pi\_\{t\}\; =\; f(u\_\{t\})\; +\; a\; pi\_\{t\}^e$

$pi\_\{t+1\}\; =\; pi\_\{t\}^e\; +\; c\; (pi\_\{t\}\; -\; pi\_\{t\}^e)$





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 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

★ Feigenbaum constants

External links

★ The Flip (Period Doubling) Bifurcation in Discrete Time, Dynamic Processes