# Chaotic system w/ initial condition

by Brown Arrow
Tags: chaotic, classical mechanics, physics
 P: 101 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
HW Helper
PF Gold
P: 2,908
 Quote by 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.
Hi Arrow. I'm no expert on chaotic systems but isn't a pencil balanced on its point a chaotic system?
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?
 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 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.
 PF Gold P: 961 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 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.

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