logistic: Plot chaotic logistic growth

In mariodosreis/fractal: Fractal

Plot chaotic logistic growth

Description

Plot chaotic logistic growth

Usage

logistic(
  x.init = 0.01,
  gen = 50,
  rlim = c(3.2, 4),
  ylim = c(0, 1),
  pch = ".",
  col = rgb(0, 0, 0, 0.3),
  div = 2000,
  k = 32
)

Arguments

x.init	numeric, the initial population size, X(0)
gen	numeric, the number of generations
rlim	numeric, the growth rate, r, range, for plotting
ylim	numeric, the y-axis limits, for plotting
pch	the plotting character for points
col	the plotting color for points
div	numeric, the number of divisions along the x-axis, for plotting
k	numeric, the number of burn-out generations Consider a population with growth X(t+1) = r * X(t) * (1 - X(t)) where r is the growth rate and X(t) is the population size at generation t, with 0 <= X(t) <= 1. This equation shows chaotic behaviour for r > 3.57. For example, for r < 3, the population growths until converging to a limit. For 3 < r < 3.57 the population oscillates between two values. Beyond r = 3.57, the behaviour becomes chaotic. This function plots the long-term values of X(t) as a function of r.

Author(s)

Mario dos Reis

References

Tien-Yin Li and James A. Yorke. (1975) Period three implies chaos. The American Mathematical Monthly, 82: 985–992.

May R. (1976) Simple mathematical models with very complicated dynamics. Nature, 261: 459–467.

Examples

logistic()

## Not run: 
# higher resolution but slow
logistic(div=4000, k=128)

## End(Not run)

mariodosreis/fractal documentation built on March 19, 2024, 3:28 p.m.