Binary Coding Functions for Generalized Logistic Maps with z-Unimodality
Binary Coding Functions for Generalized Logistic Maps with z-Unimodality
This Demonstration shows binary coding functions for one-dimensional iterative maps with -unimodality [1]. The test map, ()==λ(1-|)2-1, generalizes the classic logistic map, ()==λ(1-) [12–15]. Here is the iteration number, is the iterate of () starting from the initial value (i.e. =∘∘⋯∘()=()), is the main control parameter, and is the subcontrol parameter ( determines the unimodality, the degree of the local maximum of ()).
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th
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(n)
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λ
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This Demonstration uses one of three coding functions
1
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∑
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∏
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∑
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(-1)
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where (x) is a unit-step function satisfying
A
σ
A
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0 | if | x<0 |
1 | if | x≥0 |
and (x) is another step function (a sign function) satisfying
B
σ
B
σ
A
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-1 | if | x<0 |
+1 | if | x≥0 |
The blue box on the left is a Locator that you can drag; the image inside the box is rescaled on the right in accordance with the zoom-in level . The binary coding function () (, , or ) acts on 251 (or 2001) equally spaced initial condition for both plots.
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