What is the difference between nonlinearity and chaos, or . . . .

Main Question or Discussion Point

What is the difference between nonlinearity and chaos, or is there a difference?
 

Answers and Replies

1,222
2
Not all nonlinear systems of eqs are chaotic.
 
372
0
You're asking the question the wrong way round. A more logical question would be "under what conditions are they the same?"

As it stands, the shortest answer would be "they're not the same thing". Chaos is a different phenomenon to nonlinearity, but sometimes arises from it.
 
vanesch
Staff Emeritus
Science Advisor
Gold Member
5,007
16
What is sure, is that chaotic systems are non-linear.

The definition of a chaotic system is:
- exponential divergence of initially close orbits (Liapunov instability)
- the state of the system remains in a compact space

Well, you cannot satisfy both with a linear system: in the case there is exponential divergence, at least one solution will become unbounded.
 

Related Threads for: What is the difference between nonlinearity and chaos, or . . . .

  • Last Post
Replies
18
Views
3K
  • Last Post
Replies
1
Views
632
Replies
1
Views
578
Replies
7
Views
1K
  • Last Post
Replies
4
Views
549
Replies
9
Views
6K
  • Last Post
Replies
4
Views
2K
Replies
8
Views
857
Top