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Chaotic system w/ initial condition 
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#1
Apr912, 03:25 PM

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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 nonchaotic?
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 


#2
Apr912, 05:31 PM

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Ref: RIGB.org The Frontiers of Science If so, then what happens if the initial conditions of the perfectly vertical pencil were to be changed? 


#3
Apr912, 05:40 PM

P: 101

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


#4
Apr912, 06:30 PM

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Chaotic system w/ initial condition
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 nonchaotic attractor (say, a fix point) then there obviously must be some initial conditions, namely those in the basic of attraction for this nonchaotic attractor, that will lead to a nonchaotic trajectory.
For the Duffing Oscillator (Duffing's Equation) I believe there are parameters for which the system has both chaotic and nonchaotic trajectories, and in those cases you will get chaotic or nonchaotic trajectory depending on the initial conditions. For instance, it looks like there should be both a chaotic and nonchaotic 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. 


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