RE: Nonlinear Dynamical Systems: Chaos Theory, Models and the Butterfly Effect by mathowl

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steemstem · @mathowl · Jun 5 '18 (edited)

Good job in correcting it.

I am still not sure what you mean with nonlinear factor. A linear and a nonlinear system can both exhibit periodic behaviour. In the linear case just consider the discrete dynamical system with phase space \mathbb{R} / \mathbb{Z}  and evolution operator x \mapsto a x where a is a real non-zero constant. The evolution operator is linear and it exhibits periodic behaviour.

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@obamike · Jun 5 '18

You are right; a periodic system can be linear or nonlinear. With nonlinear term, I am referring to the function that specifies the change in the system. That is, the rule governing the system must contain nonlinear term.
<br>

So sorry for my belated response, I have to teach kids in a rural community every day where we hardly get internet connection. I only see comments and read post when I get home around this time.

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@mathowl · Jun 5 '18

so then the following  statement does not make any sense:

> Generally, a periodic system or quasiperiodic system must have the following properties:
>1.    At least one nonlinear factor (term) must be present in the system
 >2.    It must be at least one dimensional

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@obamike · Jun 5 '18

I really don't understand what you mean. Are you implying that a nonlinear dynamical system cannot be periodic or quasiperiodic? because then what I have been reading in various text will be false.
>I hope you know I am talking about periodic and quasiperiodic systems in terms of nonlinear system as my topic imply and not linear system?

<br>
What I am saying in a nutshell is that the equation of motion for nonlinear systems will have at least one term that is either a square or higher power, a product of two or more variables of the system or even a more complicated function etc.

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