Why Is Chaos Deterministic and Not Random?

[student-engineer]

Chaos is deterministic behavior.Why is chaos deterministic.Why chaos is not random.
Chaos is sensitive dependence on initial conditions,a slight change in initial condition can give rise to totally different trajectories.

 

[jedishrfu]

Systems have three modes of operation:
- predictable (linear)
- chaotic (nonlinear)
- random (random)

Chaos appears between the predictable mode and the random mode. In a sense, chaos provides a wider envelope of motion for a system where we can't predict the motion but we know the motion won't go outside the envelope either. Also in chaotic systems we may see patterns that appear for a time and then new patterns emerge.

Buildings sway in any wind. For small winds, the sway is pretty linear, pretty predictable. For larger winds, the sway becomes chaotic, not predictable but within the engineering limits (envelope of motion) of the building. For really large winds, the building may be driven beyond chaotic to random and then failure occurs and the building collapses.

https://en.wikipedia.org/wiki/Chaos_theory

Chaos vs Random

http://faculty.rhodes.edu/wetzel/random/level23intro.html

https://en.wikipedia.org/wiki/Randomness

 

[student-engineer]

Systems have three modes of operation:
- predictable (linear)
- chaotic (nonlinear)
- random (random)

Chaos appears between the predictable mode and the random mode. In a sense, chaos provides a wider envelope of motion for a system where we can't predict the motion but we know the motion won't go outside the envelope either. Also in chaotic systems we may see patterns that appear for a time and then new patterns emerge.

Buildings sway in any wind. For small winds, the sway is pretty linear, pretty predictable. For larger winds, the sway becomes chaotic, not predictable but within the engineering limits (envelope of motion) of the building. For really large winds, the building may be driven beyond chaotic to random and then failure occurs and the building collapses.

https://en.wikipedia.org/wiki/Chaos_theory

Chaos vs Random

http://faculty.rhodes.edu/wetzel/random/level23intro.html

https://en.wikipedia.org/wiki/Randomness

Random is something which is not predictable.Chaotic trajectories are also not predictable,so why is chaos not random.

In the article http://faculty.rhodes.edu/wetzel/random/level23intro.html it is also mentioned,' Chaos theory has shown that deterministic systems can produce results which are chaotic and appear to be random. But they are not technically random because the events can be modeled by a (non-linear) formula.'
Is this the reason

 

[jedishrfu]

The chaotic trajectory isn't predictable over a longer period of time but it still operates in a given envelope of motion whereas random motion has no such envelope. Think of the building example I gave.

 

[anorlunda]

The picture is an example of chaotic behavior. We can't predict the exact path in the future, but it is also clear from the picture that the behavior is not random. Below is an example of random.

 

[student-engineer]

Thank you @jedishrfu and @anorlunda