Things to know about Chaos:

Practice problems

1. Below are tables showing values for two iterated functions. For each function, tell whether it appears to be a chaotic function or not, and why you think so (all of the numbers are percents of the maximum capacity of the environment)

Iteration number
Function A
Function A
Function B
Function B
1
.240
.250
.240
.250
2
.511
.525
.638
656
3

.700
.698
.808
.790
...
...
...
...
...
14
.637
.638
.385
.461
15
.647
.647
.829
.870
16
.639
.639
.496
.396

2. A. Using the population simulation equation:

Pn+1 = (1-Pn)*Pn*3+Pn, starting with the value P0 = .250. Find the first 5 iterations of this function (round to 3 decimal places). Does it appear to be staying near a particular value or values? If so, tell what value it is getting close to.

B. Using the population simulation equation:

Pn+1 = (1-Pn)*Pn*2+Pn, starting with the value P0 = .250. Find the first 5 iterations of this function (round to 3 decimal places). Does it appear to be staying near a particular value or values? If so, tell what value it is getting close to.

Answers