# Numerical Integration of the Logistic Equation Using Runge-Kutta Methods

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The continuous logistic model is described by the differential equation , where is known as the Malthusian parameter. This Demonstration allows you to integrate this DE numerically with several Runge–Kutta methods with orders from 1 up to 3, with constant step size and initial value . This procedure illustrates chaos and bifurcation. In particular, by using the Euler method, the map is very similar to the classic logistic map, but other RK methods give different and more interesting maps.

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Contributed by: Luis Rández (January 2012)

Based on programs by: Robert M. Lurie

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This formulation is modified from that given in [1], p. 941 ff.

Reference

[1] H. Ruskeepää, *Mathematica Navigator*, 3rd ed., San Diego: Academic Press, 2009.

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