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The animation shows the change in behavior as the parameter (r in the figure) is increased from 1 to 4, starting from an initial value of 0.2.) The logistic map is a discrete dynamical system defined by the quadratic difference equation:
Value-stream mapping has supporting methods that are often used in lean environments to analyze and design flows at the system level (across multiple processes).. Although value-stream mapping is often associated with manufacturing, it is also used in logistics, supply chain, service related industries, healthcare, [5] [6] software development, [7] [8] product development, [9] project ...
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
An animated cobweb diagram of the logistic map = (), showing chaotic behaviour for most values of >. A cobweb plot , known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions , such as the logistic map .
A = 0, all other parameters are 1. The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves.
Typically, supply-chain managers aim to maximize the profitable operation of their manufacturing and distribution supply chain. This could include measures like maximizing gross margin return on inventory invested (balancing the cost of inventory at all points in the supply chain with availability to the customer), minimizing total operating expenses (transportation, inventory and ...
The tent map with parameter μ = 2 and the logistic map with parameter r = 4 are topologically conjugate, [1] and thus the behaviours of the two maps are in this sense identical under iteration. Depending on the value of μ, the tent map demonstrates a range of dynamical behaviour ranging from predictable to chaotic.
As the logistic distribution, which can be solved analytically, is similar to the normal distribution, it can be used instead. The blue picture illustrates an example of fitting the logistic distribution to ranked October rainfalls—that are almost normally distributed—and it shows the 90% confidence belt based on the binomial distribution.