Difference between revisions of "Logistic"
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D. Kouznetsov. Holomorphic extension of the logistic sequence. |
D. Kouznetsov. Holomorphic extension of the logistic sequence. |
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Moscow University Physics Bulletin, April 2010, Volume 65, Issue 2, pp 91-98. |
Moscow University Physics Bulletin, April 2010, Volume 65, Issue 2, pp 91-98. |
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| − | </ref>, which is quadratic function |
+ | </ref>, which is quadratic function \(T\) of special kind: |
| + | <math> |
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| − | $$ |
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T(z)=q\cdot z \cdot (1-z) |
T(z)=q\cdot z \cdot (1-z) |
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| + | \</math> |
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| − | $$ |
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| − | where |
+ | where \(q\) is constant. Usually it is assumed that \(q\) is real. [[Logistic operator]] can be considered as a [[transfer function]] for simple model of the system with chaotic behavior. [[Superfunction]]s \(F\) for the [[Logistic operator]], id est, [[holomorphic function|holomorphic]] solution \(F\) of equation |
| − | + | <math> F(z\!+\!1)=T(F(z)) |
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| + | \</math> |
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| − | $$ |
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| − | can be constructed in a standard way, using the [[fixed point]]s |
+ | can be constructed in a standard way, using the [[fixed point]]s \(0\) or \(q\!-\!1\). The [[superfunction]] allows to express the [[regular iteration]] of the [[logistic operator]] in the following way: |
| + | <math> |
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| − | $$ |
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T^c(z)=F(c+F^{-1}(z)) |
T^c(z)=F(c+F^{-1}(z)) |
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| + | \</math> |
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| − | $$ |
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| − | where |
+ | where \(F^{-1}\) is [[inverse function]] of \(F\); in wide range of values of \(z\), the relation \(F(F^{-1}(z))=z\) |
holds. |
holds. |
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Cars H.Hommes. |
Cars H.Hommes. |
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Adaptive learning and roads to chaos. (1990). .. The dynamics of the expected prices in the model is |
Adaptive learning and roads to chaos. (1990). .. The dynamics of the expected prices in the model is |
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| − | described by a one-dimensional nonlinear difference equation |
+ | described by a one-dimensional nonlinear difference equation \(x_{n+1}=f(x_n)\). Chiarella (1988) approximated this model by the well known logistic map \(x_{n+1}=\mu x_n (1-x_n)\).. |
http://csc.ucdavis.edu/~cmg/papers/EoMfaDS.pdf |
http://csc.ucdavis.edu/~cmg/papers/EoMfaDS.pdf |
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James P. Crutchfield and Bruce S. McNamara. Equations of Motion from a Data Series. (1987–2013) |
James P. Crutchfield and Bruce S. McNamara. Equations of Motion from a Data Series. (1987–2013) |
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.. |
.. |
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| − | The first example shows the effect of extrinsic noise on the model entropy and the optimum model. We consider the stochastic logistic map |
+ | The first example shows the effect of extrinsic noise on the model entropy and the optimum model. We consider the stochastic logistic map \(x_{n+1} = r x_n(1−x_n) + ξ_n\) where the nonlinearity parameter r is 3.7, so that the deterministic behavior is chaotic. .. |
==Keywords== |
==Keywords== |
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Latest revision as of 18:26, 30 July 2019
Term Logistic is ambiguous.
In administration, Logistic is detailed organization and implementation of a complex operation [1]; detailed coordination of a complex operation involving many people, facilities, or supplies [2]. Also, Logistics is the management of the flow of resources between the point of origin and the point of consumption in order to meet some requirements, for example, of customers or corporations.[3]
In science, Logistic may refer to the logistic operator [4], which is quadratic function \(T\) of special kind\[ T(z)=q\cdot z \cdot (1-z) \\] where \(q\) is constant. Usually it is assumed that \(q\) is real. Logistic operator can be considered as a transfer function for simple model of the system with chaotic behavior. Superfunctions \(F\) for the Logistic operator, id est, holomorphic solution \(F\) of equation \( F(z\!+\!1)=T(F(z)) \\) can be constructed in a standard way, using the fixed points \(0\) or \(q\!-\!1\). The superfunction allows to express the regular iteration of the logistic operator in the following way\[ T^c(z)=F(c+F^{-1}(z)) \\] where \(F^{-1}\) is inverse function of \(F\); in wide range of values of \(z\), the relation \(F(F^{-1}(z))=z\) holds.
References
- ↑ http://oxforddictionaries.com/definition/english/logistics
- ↑ Mark Hershberger. The detailed coordination of a complex operation involving many people, facilities, or supplies. Mediawiki, 18 May 2013.
- ↑ http://en.wikipedia.org/wiki/Logistics
- ↑
http://www.ils.uec.ac.jp/~dima/PAPERS/2009logistie.pdf
http://dx.doi.org/10.3103/S0027134910020049 D. Kouznetsov. Holomorphic extension of the logistic sequence. Moscow University Physics Bulletin, April 2010, Volume 65, Issue 2, pp 91-98.
http://dare.uva.nl/document/15299
Cars H.Hommes.
Adaptive learning and roads to chaos. (1990). .. The dynamics of the expected prices in the model is
described by a one-dimensional nonlinear difference equation \(x_{n+1}=f(x_n)\). Chiarella (1988) approximated this model by the well known logistic map \(x_{n+1}=\mu x_n (1-x_n)\)..
http://csc.ucdavis.edu/~cmg/papers/EoMfaDS.pdf James P. Crutchfield and Bruce S. McNamara. Equations of Motion from a Data Series. (1987–2013) .. The first example shows the effect of extrinsic noise on the model entropy and the optimum model. We consider the stochastic logistic map \(x_{n+1} = r x_n(1−x_n) + ξ_n\) where the nonlinearity parameter r is 3.7, so that the deterministic behavior is chaotic. ..
Keywords
Administration, Logistic sequence, Logistic operator, Superfunction, Ambiguity,,