Chen-Celikovsky Attractor | Chaotic attractor | Chaos Theory

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This nonlinear system with specific initial conditions is solved
numerically and the resulting trajectory is shown through a 3 dimensional animation.
[www.3d-meier.de...]
Initial condition 1: (1. ,1., 1.05)
Initial condition 2: (1.05,1., 1. )
"When the parameters a = 36 and b = 3 are fixed while parameter c varies, one can observe that the attractor generated by this system is similar to the Lorenz attractor for c in (12.7 -17.0), has a transitory shape when 'c' is between 18.0 to 22.0, and then becomes similar to Chen’s attractor when 'c' is in range of 23.0 - 28.5"
Reference: A NEW CHAOTIC ATTRACTOR COINED JINHU LÜ, GUANRONG CHEN
International Journal of Bifurcation and Chaos, Vol. 12, No. 3 (2002) 659-661
lsc.amss.ac.cn/...
In 1963, Lorenz reported the first chaotic attractor in a three-dimensional autonomous system [Sparrow, 1982].
Since Lorenz found the first chaotic attractor in a smooth three-dimensional autonomous system, later chaotic attractors were developed, for example the Rossler system, the Sprott system, the Chen system, the Lu system, the generalized Lorenz system family, and the hyperbolic type of the generalized Lorenz canonical form. Here one of such attractor is shown in this video.
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#ChenCelikovsky|#ChaoticSystem #ButterflyEffect| thinkeccel

Опубликовано:

27 сен 2024

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Комментарии : 7

@archonphilosopher8221 Год назад

Okay. Thank you for the wonderful transportation from a mathematical format to a design format. The clavis (key) however is to find where in the natural world such a mathematical formula makes its appearance, if any. It seems clear that we could not identify such a pattern until mathematically we had the vocabulary, as was the case with the Fibonacci Sequence. I would appreciate any information on how this, or indeed any other Attractor, strange or otherwise, making its appearance in the world as measurable. For those interested, it appears that ontologically (dealing with Being), Attractors are a structural feature at multiple levels affecting both raw matter and sentient behaviors. Notably, Daniel Dennett has proposed the Intentional Stance as that essential feature of consciousness that necessarily moves out of itself, as if "attracted" or "bound by enchantment" [not his terms] towards instantiating the Being of whatever is. For those still interested, it appears as if the Universe Itself Is A Strange Attractor, and that our field of experience is peppered with hidden attractors, the harnessing of which remains outside of human powers. However, it may be the case that other sentient creatures are able to either or both navigate or/and direct the functioning of Attractors for their purposes. For example, if one identifies a process as following the Fibonacci Sequence or attuned to the Feigenbaum Constant, then one has a good idea of where to look to gain "the prize", while others are as groping in the dark. All the best and thank you again for the video and the instruction to comment.