What is the logistic map used for?

This so-called “logistic map” has been used as model for population dynamics, but here we just treat it as a toy model which has a transition to chaos. f X X It is best to see successive iterations graphically, i.e. Since f'(x) = 4 Λ (1 – 2x), the fixed point at x = 0 is stable when 4Λ < 1, i.e. Λ < 0.25.

What is the logistic map equation?

The logistic map is a one-dimensional discrete-time map that, despite its formal simplicity, exhibits an unexpected degree of complexity. The logistic map is defined by the following equation: x n + 1 = λ x n ( 1 − x n ) with n = 0 , 1 , 2 , 3 . . . x_{n+1}=\lambda x_{n}(1-x_{n})\quad\text{with}\quad n=0,1,2,3…

Why does the logistic map end at 4?

As r rises there is a succession of new windows with different c values. The first one is for c = 1; all subsequent windows involving odd c occur in decreasing order of c starting with arbitrarily large c. Beyond r = 4, almost all initial values eventually leave the interval [0,1] and diverge.

Who created the logistic map?

Ricker in 1954 and detailed analytic studies of logistic maps beginning in the 1950s with Paul Stein and Stanislaw Ulam that the complicated properties of this type of map beyond simple oscillatory behavior were widely noted (Wolfram 2002, pp. 918-919).

Is logistic equation chaotic?

This equation was a simple quadratic equation called the logistic difference equation. On the surface, one would not expect this equation to provide the fantastically complex and chaotic behavior that it exhibits.

What is supply chain mapping?

What is supply chain mapping? Mapping your supply chain means gathering information about your suppliers, their own suppliers, and the people who work in your supply chain to create a global map of your supply network. This information can be held in a single data platform for ease and to facilitate analysis.

How do I create a logistics map in Excel?

Create Logistic Plot

1. Launch Microsoft Excel and load a worksheet with existing data or create a new worksheet.
2. Click on the “Insert” tab and select a chart style beneath the Charts heading.
3. Input the cell range for the x and y data values for your logistic growth curve.
4. Use an existing time base or create a new one.

What are chaotic maps?

In mathematics, a chaotic map is a map (= evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Chaotic maps often occur in the study of dynamical systems. Chaotic maps often generate fractals.

What does a bifurcation diagram show?

In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system.

Is the logistic map a fractal?

This is the logistic map: . It is a fractal, as some might know here. It has a Hausdorff fractal dimension of 0.538.