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Logistic Equation r=4
释义
Logistic Equation
r
=4
With
, the Logistic Equation becomes
(1)
Now let
(2)
(3)
(4)
(5)
Manipulating (2) gives
(6)
so
(7)
(8)
But
. Taking
, then
and
(9)
For
,
and
(10)
Combining
(11)
which can be written
(12)
the Tent Map with
, so the Natural Invariant in
is
(13)
Transforming back to
gives
(14)
This can also be derived from
(15)
where
is the Delta Function.
See also
Logistic Equation
随便看
Iterated Exponential Constants
Iterated Function System
Iterated Radical
Iteration Sequence
Itô's Lemma
Itô's Theorem
Iverson Bracket
Iwasawa's Theorem
j
Jackson's Difference Fan
Jackson's Identity
Jackson's Theorem
Jacobi Algorithm
Jacobian
Jacobian Conjecture
Jacobian Curve
Jacobian Determinant
Jacobi-Anger Expansion
Jacobian Group
Jacobi Differential Equation
Jacobi Differential Equation (Calculus of Variations)
Jacobi Elliptic Functions
Jacobi Function of the First Kind
Jacobi Function of the Second Kind
Jacobi-Gauss Quadrature
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更新时间:2024/11/15 2:39:48