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181:. The technique was introduced in the 1890s by E.-M. LĂ©meray. Using a cobweb plot, it is possible to infer the long term status of an
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is represented by a rectangle, while greater period cycles produce further, more complex closed loops. A
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corresponds to the segment of the staircase with progressively decreasing stair lengths or to an inward
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Construction of a cobweb plot of the logistic map y = 2.8 x (1-x), showing an attracting fixed point.
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Plot vertically from the point on the diagonal to the function curve. This has the coordinates (
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orbit would show a 'filled out' area, indicating an infinite number of non-repeating values.
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Plot horizontally across from this point to the diagonal line. This has the coordinates (
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Find the point on the function curve with an x-coordinate of
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to investigate the qualitative behaviour of one-dimensional
222:{\displaystyle f:\mathbb {R} \rightarrow \mathbb {R} }
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57:. Unsourced material may be challenged and removed.
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632:] (in German). Birkhäuser Basel. p. 8.
597:"Sur la convergence des substitutions uniformes"
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604:Nouvelles annales de mathématiques, 3e série
626:Berechenbares Chaos in dynamischen Systemen
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149:behaviour for most values of r > 3.57.
117:Learn how and when to remove this message
624:Stoop, Ruedi; Steeb, Willi-Hans (2006).
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185:under repeated application of a map.
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521:{\displaystyle f(x_{0}),f(f(x_{0}))}
55:adding citations to reliable sources
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630:Computable Chaos in dynamic systems
290:. To plot the behaviour of a value
229:, the plot consists of a diagonal (
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141:An animated cobweb diagram of the
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540:On the LĂ©meray diagram, a stable
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451:{\displaystyle f(x_{0}),f(x_{0})}
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531:Repeat from step 2 as required.
42:needs additional citations for
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390:{\displaystyle x_{0},f(x_{0})}
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740:Mathematical physics stubs
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595:LĂ©meray, E.-M. (1897).
145:y = r x (1-x), showing
679:-related article is a
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283:{\displaystyle y=f(x)}
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638:10.1007/3-7643-7551-5
572:Fixed-point iteration
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341:{\displaystyle x_{0}}
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735:Dynamical systems
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159:LĂ©meray Diagram
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68: –
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66:"Cobweb plot"
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62:Find sources:
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40:This article
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685:expanding it
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179:logistic map
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143:logistic map
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49:Please help
44:verification
41:
542:fixed point
171:mathematics
155:cobweb plot
107:August 2014
724:Categories
610:: 306–319.
582:References
77:newspapers
212:→
169:field of
560:See also
554:chaotic
147:chaotic
91:scholar
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546:spiral
189:Method
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675:This
628:[
600:(PDF)
550:orbit
98:JSTOR
84:books
681:stub
642:ISBN
70:news
634:doi
161:or
53:by
726::
640:.
616:^
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153:A
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216:R
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95:·
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