Questions tagged [nonlinear-dynamics]

This tag is for questions relating to nonlinear-dynamics, the branch of mathematical physics that studies systems governed by equations more complex than the linear, $~aX+b~$ form.

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Dynamics of a sliding cube on the $XY$ and $YZ$ planes

A cube with side length $a$, is initially placed with one vertex at the origin, and its faces parallel to the coordinate planes ($XY, XZ, YZ$) and totally lying in the first octant. Then its rotated ...
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How to approximate any line segment within a circular region using the minimum number of connected rotating axes

This problem arises from my personal experience in developing a game mod. At that time, I wanted to create a drone system for vehicles, but due to the limitations of the game itself, I could only ...
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Can probe trajectories to compute Lyapunov exponents get "stuck in more regular orbits" after rescaling?

I am computing Lyapunov exponents, and there is something that I do not understand about the data. The model has a regime for $\delta \approx 1$ (in some units) where it is fully chaotic, and the ...
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I have been trying to solve the following question but i am very unsure about my solution, can someone help me with it? Consider a bead of mass $m$ that slides along a circular rigid wire hoop of ...
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A question on the qualitative analysis of solution of a system of ODEs [closed]

Let $f:\mathbb{R}^2 \to \mathbb{R}^2$ be a non-zero smooth vector field satisfying $\text{div} f \ne 0.$ Which of the following are necessarily true for the ODE: $\dot{\mathbf{x}}=f(\mathbf{x})$? (a) ...
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Mean, Variance and Correlation Function of a quadratic SDE

I am struggling with the following nonlinear SDE: $ds=dt(-\Omega s^2(t)+\alpha s(t)+\beta) + d\xi(t)(\gamma (1-s(t)))$ $d\xi = dt(-\frac{1}{\tau} \xi(t)) + \sigma dW(t)$ Where $\alpha$, $\Omega$, ...
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Example 1.2 Nonlinear Control Khalil

$f( x) =\begin{bmatrix} x_{2}\\ -sat( x_{1} +x_{2}) \end{bmatrix}$ is not continuously differentiable on $R^2$. Using the fact that the saturdation function sat(.) satisfies $|sat(\eta)-sat{\xi}|$, we ...
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