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RE: Nonlinear Dynamical Systems: Chaos Theory, Models and the Butterfly Effect
I am still talking about this part of your post->
A periodic system or quasiperiodic system must have the following properties:
- At least one nonlinear factor (term) must be present in the system
- It must be at least one dimensional
So you said you were only considering non-linear systems for this statement.
My claim is that this statement gives no information for non-linear systems since all non-linear systems automatically satisfy both 1 and 2.
I have no idea for a reference but the proof is almost immediate. Since you only need to show that non-linear dynamical systems cannot have dimension 0.
(Note that in the above I am considering a phase space which is an open subset of \mathbb{R}^n. I am also assuming that you are considering a connected phase space)
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Teacher(me): students the characteristics of living things include: Movement, Respiration, Irritability, growth, etc..
I then ask a question, what are the characteristics of a dog?
Student: movement, respiration, irritability, growth...etc
Teacher (me): It doesn't make sense since all living things has this properties.
This gives no information for a dog
Alright, I didn't just stop after mentioning this properties for periodic and quasiperiodic systems, I also say the same for chaotic and hyperchaotic systems. I have not left any nonlinear dynamical system out in my description so what is my crime?
You can tell that is a general property, what if I have left that out and some other reader who is not well vast or doesn't even know about nonlinear system as much as you reads and that information is not there?
Whatever I write are things I read in the course of my study and I am still studying.
With due respect sir, I hope you don't have something against me? because I can't help but noticed that you are dragging me back and forth.
If you have something you wish to tell me please feel free...I love honest feedback.
I just want your post to be correct and have meaning.
Using your example it is not usefull to say that a dog is a thing. This gives almost no information. The same is true for the point 1 and 2 in the earlier statement.
So my post is not correct and doesn't have meaning?
please note, it is useful to say that a dog is a living thing! What is useful is relative!