Simulation Outline

[MKLau]

• Using a fixed distance as determined by the maximum distance possible from the 4th attractor set into chaos, set the initial r value and the final r value.
• Choose a set of random x0
• Choose an arbitrary number of iterations in the initial state
• Generate a set of x values
• Update r to the final r
• Generate a set of x values using the same arbitrary number of iterations from the first set
• Repeat for each threshold

[MKLau]

Repeat and vary the number of iterations within each system state

[MKLau]

Repeat but this time change the system state across two boundaries

[MKLau]

Repeat but this time go down in system state (e.g., two to one attractors or chaos to two attractors).

[MKLau]

[MKLau]

Attractor numbers and associated r ranges

a rl ru

[1] 1.004 2.995

[2] 3.003 3.447

[4] 3.451 3.543

[8] 3.545 3.569

[MKLau]

Using the above distance of 3.545 to 3.569 (i.e., 0.024), we can set the maximum step size equal to 0.048, which is double 0.024.