# Tagged Questions

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### What methods can I use to model a seemingly chaotic set of values? [closed]

If I have a graph/set of data, what methods can I use to model the data to predict a likely next set of values? For example, given the following numbers [ 2, 4, 5, 2, 1, -1, -2, 0 ], are there some ...
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### Quantifying Poincare map

I have a dynamical system which goes from chaos to ordered state (quasiperiodic state to be precise). I have represented this transition via a Poincare map. See the attached figures. Now, my question:...
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### Strange behavior of $\sin(x^3)$ and $\tan(x^3)$

I noticed this behavior a long time ago and never really figured this out but if you take the $\sin$ or $\cos$ or $\tan$ etc. of a cubic polynomial you get a very strange and erratic behavior. It ...
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### Chaotic neural network - help in understanding

I am having difficulty in understanding a technique for clustering and segmentation of biomedical images using the concept of time series. The paper on which the Question is based is : M. Lacomi et. ...
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### What's the name of this chaotic system? (Cool pics included.)

I found this playing with a 2D-ODE-system plotter I'm writing. Surely, since it's so simple, it's been found and extensively studied by someone. What's it called? I'd like to look it up and learn a ...
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### How to numerically find Floquet multipliers (e.g., characteristic multipliers or Lyapunov exponents for periodic orbits from chaotic systems)?

Anyone have any suggestions for the following situation/question? (help wanted, please!) I understand the theory (c.f., Perko or Nayfeh and Balachandran, Ch.3), but I do not understand how this is ...
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### Period 2 orbit of logistic map?

Suppose that G: $\mathbb R$ $\rightarrow$ $\mathbb R$ such that G(x)=4x(1-x). I need to find the period 2 orbit(s?) of this map and decide if it's a sink or a source. If I could find the fixed points ...
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### Example of a continuous function with only one fixed point and no periodic points

Does anyone know how to go about finding an example of a function with no periodic point and only one fixed point. This f is continuous in an interval I, and I c f(I). As an addendum, can this fixed ...
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### Prove that the tent map has exactly nine 6-cycles.

Prove that the tent map T(x)= {2x if 0<=x<=1/2 and 2-2x if 1/2
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### Finding periodic points of every period, Sharkovskii's Theorem

Consider the map: $C_c(x)=c\cos(x)$ (a) Find a value of the parameter c for which this map has prime periodic points of every period, and provide an explanation with graphs supporting your argument. ...
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### Isolated Versus Non-Isolated Fixed Point, 2D Dynamics

I am trying to understand the classification of fixed points in a dynamical systems context (fixed points of a system of two linear differential equations are places where both $x_1' = x_2' = 0$). ...
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### Cat map like maps without period

Is there any area-preserving chaotic map other than Arnold cat map which can be applied on a rectangle as well as being reversible but not periodic?
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### The extent of chaos

In chaotic systems the typical situation is that at a low level trajectories of points are wild, but overall there is a nice statistical description of the system. For example, consider the ...