Logistic map

The logistic map is a discrete dynamical system defined by the quadratic difference equation:

${\displaystyle x_{n+1}=rx_{n}(1-x_{n}),}$

1

Equivalently it is a recurrence relation and a polynomial mapping of degree 2. It is often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations.

The map was initially utilized by Edward Lorenz in the 1960s to showcase properties of irregular solutions in climate systems.^[1] It was popularized in a 1976 paper by the biologist Robert May,^{[May, Robert M. (1976) 1]} in part as a discrete-time demographic model analogous to the logistic equation written down by Pierre François Verhulst.^[2] Other researchers who have contributed to the study of the logistic map include Stanisław Ulam, John von Neumann, Pekka Myrberg, Oleksandr Sharkovsky, Nicholas Metropolis, and Mitchell Feigenbaum. ^{[3][citation needed]}

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