Question

Problem G) Consider the non-linear dynamical system an+1 = r(1 − an)an. In class we discovered that the behavior was simple when r < 3, but started being chaotic at around r = 3.57. Let r = 3.83 and ao = 0.5. Use a calculator to find the first 20 values of an. Is there a pattern forming? If so, how would you classify the pattern? Keeping r = 3.83, try using a different value of a0 between 0 and 1. Again, use a calculator find the first 20 values of an. (It may take a few more to establish the behavior.) Is there the same behavior as when a0 = 0.5? Would you classify this behavior as stable or unstable?

Problem H) Repeat problem G, except use r = 3.739.

math modeling Please Help with Both !!

Answer 1

You can start with the given equation, since it's a chaotic dynamics it depends upon initial conditions, let's have the analysis here .you can match these values from computer program (written in Python)

So let's see the same logic in logistic maps

1.for ao=0.5 and r=3.83

Focus on the right one, you can see the period of the dynamics is 3 and it is stable.

Let's check for a0=0.3 for same r and let's see what happens

Ooo, now the pattern is gone and lots of value are here.

Let's see what happens when the time increases.

Ohh, again the steady state is reached, actually the initial randomness is call transition state .