Chaotic system w/ initial condition

[Brown Arrow]

so i have been studying chaotic system in class, and i just want to know if we change the initial conditions of a chaotic system can it become non-chaotic?

I think yes because, chaotic system is sensitive to initial condition hence it would have an effect on the chaotic behavior.

I'm I right? i have a feeling I'm wrong.


:/ I'm contradicting my self

 

[Q_Goest]

so i have been studying chaotic system in class, and i just want to know if we change the initial conditions of a chaotic system can it become non-chaotic?

I think yes because, chaotic system is sensitive to initial condition hence it would have an effect on the chaotic behavior.

Hi Arrow. I'm no expert on chaotic systems but isn't a pencil balanced on its point a chaotic system?
Ref:
http://www.rigb.org/christmaslectures06/pdfs/why_does_it_always_rain.pdf
The Frontiers of Science
If so, then what happens if the initial conditions of the perfectly vertical pencil were to be changed?

 

[Brown Arrow]

thanks for the reply Q Goest.

umm yes that is true it will no longer be chaotic.

guess i did not specify the system :/

I had a damped driven pendulum and Duffing Oscillator,

I ran some plotting (in python) for it and changed the initial condition. what once was a chaotic system became non-chaotic after the change in initial condition.

so is it safe to assume that chaotic system can become non-chaotic depending on the initial condition? from the reference you gave Q Goest i think the answer is yes.

 

[Filip Larsen]

In short, for a (dissipative) dynamic system with a given fixed set of parameters there can in general be one or more attractors (with at least one of these being a chaotic attractor a.k.a. strange attractor if the system is to be chaotic) each with an associated basin of attraction. If the system in addition to the chaotic attractor(s) has a non-chaotic attractor (say, a fix point) then there obviously must be some initial conditions, namely those in the basic of attraction for this non-chaotic attractor, that will lead to a non-chaotic trajectory.

For the Duffing Oscillator (Duffing's Equation) I believe there are parameters for which the system has both chaotic and non-chaotic trajectories, and in those cases you will get chaotic or non-chaotic trajectory depending on the initial conditions. For instance, it looks like there should be both a chaotic and non-chaotic attractor for k = 0.2 and B = 1.2 (liftet from Ueda's parameter map for Duffing's Equation as it is shown in [1]).

[1] Nonlinear Dynamics and Chaos, Thompson and Steward, Wiley, 2002.

 

[PJC01]

I can say that your thinking is on the right track. Changing the initial conditions of a chaotic system can indeed affect its behavior and potentially lead to a non-chaotic outcome. However, it is important to note that chaos is not simply determined by initial conditions alone. There are other factors at play, such as the system's parameters and external influences, that can also impact its behavior. So while changing initial conditions may have an effect, it is not a guarantee that the system will become non-chaotic. Further research and analysis would be needed to fully understand and predict the behavior of a chaotic system.