It is Funato for doubling it in a period

Funato (there is a tusk to learn divergence, period-doubling bifurcation) is a kind of the divergence for doubling it in dynamics system in a period. A stable firmness point destabilizes it when I reach the value that a parameter changes by this divergence, and there is, and two periods of stable points occur on both sides.

Specific example

${\displaystyle x}$ を real number,${\displaystyle \mu}$ Representation one-dimensional as a parameter of を real number

${\displaystyle x\to f(x,\mu) =-x-\mu x+x^{3}}$ 

I think about を. ${\displaystyle x=0}$ は${\displaystyle \mu <0}$ においては is a stable immovable point${\displaystyle f(x,\mu) =x}$ を is one period of point to satisfy),${\displaystyle \mu> 0}$ Is においては instability; again${\displaystyle \mu> 0}$ において

${\displaystyle f({\sqrt {\mu }},\mu) =-{\sqrt {\mu}}}$ 

And

${\displaystyle f(-{\sqrt {\mu }},\mu) ={\sqrt {\mu}}}$ 

であることから,${\displaystyle x=\pm {\sqrt {\mu}}}$ And it becomes the は two periods point and is stable. Therefore,${\displaystyle \mu}$ But, at a moment to step over 0 in the process that right increased from minus number, a stable firmness point (one period point) destabilized it, and two periods of points stable instead would produce it on both sides. From this, the one dimension representation mentioned above${\displaystyle \mu = 0}$ I tell the を boundary to have woken up Funato for doubling it in a period.

Allied item

• Cladogram

References

• It is science company from the (2005) "pro-dynamics divergence analysis from the new publication basics to chaotic itineracy" Motomasa Komuro

It is acquired for "doubling it https://ja.wikipedia.org/w/index.php?title= period by Funato &oldid=49222207"

This article is taken from the Japanese Wikipedia It is Funato for doubling it in a period

This article is distributed by cc-by-sa or GFDL license in accordance with the provisions of Wikipedia.

Wikipedia and Tranpedia does not guarantee the accuracy of this document. See our disclaimer for more information.

In addition, Tranpedia is simply not responsible for any show is only by translating the writings of foreign licenses that are compatible with CC-BY-SA license information.