help for ^chaos^

Iterating a logistic difference equation ----------------------------------------

^chaos , r(^#^)^ [ ^c^onnect^(^str^) s^ymbol^(^str^)^ ]

Description -----------

^chaos^ iterates for 0 < r < 4 and t = 1, 2, 3, ...

x[t+1] = r * x[t] * (1 - x[t])

starting with x[1] as a random number from the uniform distribution on [0,1).

As r increases, the generic behaviour changes from tendency to a single equilibrium to alternations between two equilibria, between four equilibria, and so on, successive bifurcations leading to `chaos' for sufficiently large r.

^chaos^ presents the user with graphs of x[t] versus t and of x[t+1] versus x[t].

Remarks -------

If there are no data in memory, ^chaos^ sets the number of observations to 200. This is suggested as a suitable number.

Options -------

^r(^#^)^ is a required option setting r: 0 < r < 4.

^connect(^ ^)^ can be used to suppress connection of data points. The default is ^l^.

^symbol(^ ^)^ can be used to specify a plotting symbol. The default is ^.^

Examples --------

. ^chaos, r(3.99)^ . ^chaos, r(3.99) c(.) sy(o)^

Author ------

Nicholas J. Cox, University of Durham, U.K. n.j.cox@@durham.ac.uk