Attractors of a time series

In summary, the conversation discusses a beginner's research on 1-Dimension time series and their chaotic characteristics. The individual hypothesizes that these differences are due to different numbers and/or types of attractors in the system. They ask for methods to observe these attractors and mention trying several techniques, including plotting Poincare plots and using a gaussian model mixture method. They also ask for help in determining if these methods are accurately identifying attractors. One suggestion is to try Ruelle-Takens embedding.
  • #1
Nono92
1
0
Hi,

I am a beginner and I don't speak very well... So I'm really sorry for my poor scientific language...

I work on 1-Dimension time series of a same system measured at different periods. In these periods, time series have different chaotic characteristics as their lyapunov exponent are different.
To explain these lyapunov exponent differences, I hypothesize the system could have different number and/or type of attractor(s). Do you think that this hypothesis could be right ?

In order to verify this hypothesis, I've tried to observe these attractors.
I don't know if it exists methods to observe it. Do you know methods to observe it ?

As I am a beginner I have tried several methods may be not adaptated.
These are the methods that I have applied :
So, I have plotted poincare plot, I have observed that at several moment there are rotations around a center.
I have calculated for each three followed points a gravity center, I have evaluated hom many cluster could be identified with a gaussian model mixture method with Calinsky Harabasz algorithm. And then I have applied gaussian model mixture with the number of clusters calculated previously on these gravity centers.

But I don't know if it is really attractors that I observe with these methods.
Could you help me ?
Thanks a lot

nono92
 
Last edited:
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What are attractors of a time series?

Attractors of a time series are mathematical concepts that describe the long-term behavior of a dynamic system. They are characterized by a small set of values that the system repeatedly approaches, regardless of the system's initial conditions.

Why are attractors important in time series analysis?

Attractors provide insight into the underlying behavior of a system, allowing us to predict future values and understand how the system responds to changes in its environment. They also help to identify patterns and trends in the data.

How do you identify attractors in a time series?

Attractors can be identified using various mathematical techniques, such as phase space analysis, Lyapunov exponents, and fractal dimensions. These methods help to visualize the behavior of the system and determine the values that it repeatedly approaches.

Can attractors change over time?

Yes, attractors can change over time as the system evolves. This can be due to external factors, such as changes in the environment or internal factors, such as feedback loops within the system. It is important to regularly analyze and update attractors to accurately predict future behavior.

What are some applications of attractors in real-world systems?

Attractors have various applications in fields such as meteorology, economics, and physics. They can be used to predict stock market trends, weather patterns, and disease outbreaks. They are also helpful in understanding chaotic systems, such as the weather or population dynamics.

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